You should be able to get a reasonable steak stovetop using a cast iron grill pan, if you have a strong enough exhaust. Oil the cast iron pan (with canola or such), then heat it very hot, until it starts to smoke. Make sure the meat is completely dry on the outside (wipe with a paper towel, water will prevent browning) and gently place in the pan. Leave it there for a minute or two (it'll smoke quite a bit!), rotate 90° to get the nice grill marks. Leave for another minute or two. Flip, and repeat for the other side.
It may splatter, have a splatter screen handy. It will smoke, quite a bit, make sure the exhaust is on high.
You will probably have a medium-rare steak now. Using a thinner cut will make it more well done (you can cut a thick steak in half with your chef's knife, making two thin steaks); so will plopping it in the oven (not sure if you want the oven before or after searing, I like 'em medium rare...).
Remember to let the meat rest for 5 minutes or so before serving.
Also, if your steaks are coming out ridiculously tough, you're probably using the wrong cut of meat, or some terrible grade. What cut are you using?
[edit: I should note that, in case it wasn't obvious, the burner should be up pretty high]
Edit by rumtscho There is a reason this answer specifies a cast iron pan. If you are limited in your cookware choice, pay attention to the maximum temperature your pan can tolerate. If you are using a non-stick pan, you have to go on medium heat and wait longer, else you'll damage the pan. (And sorry, but you can't get it as tasty as on high heat that way).
If you're trying to avoid char, then switching to honey or any sugar is probably in the wrong direction. Sugar burns...quick.
I'd recommend three things overall specific to this crust:
Use less oil. If your oil is dripping off in buckets and causing significant fires - you've got too much. Just try a light brushing on the meat.
Use a different oil. EVOO isn't recommended for grilling mostly because of it burning at lower temps. It turns black, kinda nasty, and loses all its good flavor if it goes too long, too high. You can try extra light olive oil or really just a more standard canola or peanut oil.
Use the lid on your grill. A real fire in your grill consumes oxygen fast. If you leave the lid off, it can burn for much longer. With the lid on, fires are much much shorter. I'm an avid fan of grilling with the lid on and I never knew why people complained of flair ups till I did something with the lid off, its a lot worse for flair ups.
A general steak tip, especially for something like this with a crust - make sure your steaks are at room temperature before they go on the grill. If you're starting with a cold steak, you're going to have to grill it longer and there's a much greater risk to burn the crust.
Also, consider a quick sear on each side over direct heat till your crust gets the color you want, and then move it off to indirect heat to finish.
Best Answer
To answer your question directly, if the method of cooking is what I think it is, the pan you use should be fine, even if it has a nonstick coating on it. You can read the second section to see if my assumption about your cooking method is correct.
It's important that you don't use nonstick cookware for extremely high heat cooking. If the nonstick coating gets to the smoking point, it releases gases that are toxic enough (as a friend tragically learned) to kill pets. This includes pans that go in the oven, and on the stovetop.
Since the temperature at which you're cooking the steak isn't that much hotter than you'd use baking cookies, it should be fine. If it does have a nonstick coating, you should not use it under a broiler, which is much hotter than just sitting in the oven while it bakes.
Even though it's not exactly what you asked, since you don't seem to be super confident in what you're doing, I'll give you a little more info on what I believe is the technique you're trying to pull off.
I think what you're referring to is the method of cooking where you cook a steak slowly in the oven until the internal doneness (rare, medium rare, etc.) is just how you like it, and then you give it a good hot sear in a pan so you form a flavorful crust on the outside. It's pretty intuitive when you consider the following:
You can see where the conflict lies between these two needs.
Using the method you read about, you can use the oven to gently bring it up to temperature so it's consistently cooked inside, and then you can use a pan (which does not have a nonstick coating) to give it a nice hot sear after it comes out of the oven.
It is easy to overcook steak if you're not particularly experienced, especially using more complicated dual-cook methods. Nobody wants to eat a tough, dry mess. Though it's tempting to rely on cooking times you find on the internet, time is usually the least precise method to determine how cooked something is. I highly recommend using an instant-read thermometer to check the actual temperature inside.