What is the advantage of a steel skillet over a cast iron one? I currently use cast iron for most everything and am curious what I might be missing.
Pan sauces made with wine, vinegar, or any other acid are better in stainless steel. If you put any acid in cast-iron, you are harming your seasoning, and leeching iron into your food. This will affect the taste of your sauces, I find pan sauces taste metallic when made in cast iron.
Stainless steel also heats up and cools down much faster than cast-iron. This is great when you need quick heat, or fine control of your heat. You can also plunge a piping hot stainless pan into an ice-bath without cracking it in half.
If there's an advantage to getting a steel skillet as well, what would be recommended?
Go with a a bonded stainless-steel pan with an aluminum core. The most well known manufacturer is All-Clad. The stainless steel exterior is great due to it's non reactivity, you can literally put anything in it. The aluminum core distributes the heat much more quickly and evenly, minimizing hot-spots.
Is a steel skillet good for cooking omelettes?
Not in my opinion. I go with a non-stick pan every time.
I have to recommend sticking with a nonstick pan for eggs. There's simply nothing better, although well seasoned cast iron comes awful close. If you're spending more than $20 for a nonstick egg pan, you're doing it wrong. You don't need Calphalon, or any other big name for a good nonstick pan. Go to a restaurant supply store if you can and buy a cheap one there. With care it should last you 2-5 years depending on use. I found my current one at a Bed Bath & Beyond.
All my attempts to "clean and repair" a sticky-seasoning layer have ended badly as well. I know who already snickers in the background, but my opinion is: start clean. Give the pan a lye bath and a good scrub, then reseason with a better seasoning.
"The new hotness" of flaxseed oil goes back to the fact that it doesn't go rancid easily, without heat it just dries out making a film which can protect things like wood. I bought into it, and seasoned a pan with it, and wondered why all my seasoning tries were unsucessful (I stripped and reseasoned 3 times, I think). I came to blame it on the smooth forged iron.
Then I got Cookwise and read the chapter on fats. And surprise, what does it say? That PUFA stick to everything around. (Makes sense, if you stop to think about it - those unsaturated bonds are unstable, they itch to break apart). So, when I got my next iron pan, I seasoned it with three (very thin) layers of flaxseed oil (for a solid base which will stick to the pan and the finishing layer) and then two layers of lard. After the oven, I heated it from brown to almost-black on the stove (empty).
This seasoning turned out perfect. I made crepes on it, re-oiling once every 7-8 crepes only (no fat in the batter). The pan released them like a charm. The old flaxseed-seasoned pan still sits around with some carbonized matter burnt onto the seasoning, and waits for a lye-flaxseed-lard session.
Of course, I would still take some caution with new seasoning and oil well the first few applications (I only tried the crepes after I noticed that less problematic items work great). And if you tend to often fry with the fashinably-healthy nonsaturated vegetable oils, don't heat them too much, else they could bake in a sticky-seasoning layer onto the pan. In the worst case, if you do get sticky-oil (but not carbon) buildup, try adding a new lard layer before you strip-and-reseason.
Best Answer
Pans should be completely flat, and producers are usually very good at getting it right. Even very cheaply made pans are usually sold properly flat.
What you describe sounds like you warped your pan. When you heat a pan on a burner that is too small, it becomes convex when viewed from above, if you heat it on a burner that is too large, it becomes concave. I have also seen lots of claims that heat shock (too quick heating by placing on an already hot plate, plunging into cold water right after cooking) increases warping. With thinner materials, you usually can see the warp easily with the naked eye.
I have never seen this happen in cast iron pans before (I assume here that it is really cast iron - some people call all iron pans "cast iron" although forged iron behaves differently and warps easily). Combined with you saying that you only notice it when heated, I wonder if it could be that your pan is not really warped, but only temporary developes a hump on the burner. Just try it on a fslightly large burner (which is supposed to bend the metal in the other direction) and see if it changes something.
If the pan continues to be warped when used on a different size burner, it has to be hammered flat. I have never done it myself, but the Internet is full of suggestions. They say that it can get "very flat", I have no idea if that means enough that there is no pooling, or simply much flatter than at the beginning.