It sounds to me like the issue may be that you're crowding the pan.
Basically, to get everything nice and brown and crispy, you need enough space for all of the steam to escape. That picture you showed has potatoes stacked on top of each other -- that means as the bottom items cook, they're going to end up steaming the items above them.
At a diner, they have a large griddle to work with -- they can really spread things out. You're not typically that lucky in a regular kitchen, as you don't have as much space, and you have a lip on the pans that'll hold the steam in.
So, either work in smaller batches, or consider recipes that use an oven -- using sheet pans instead of a pan on the stove solves much of the problem.
One other trick is that most diners don't start from raw potatoes -- maybe with hash browns, but not for home fries, you're not going to get the nice soft interior in a reasonable amount of time unless you start with a potato that's already been baked or boiled. (If you're doing things in the oven, you might be able to, but not in a pan)
Just for reference ... I have a 14" cast iron skillet that I use for home fries ... and it's about the right size for cooking a single large potato, which might be two servings, maybe three for kids. (I tend to cook carb-heavy meals).
update : I probably should've stated this directly -- you want the chunks of potato to form a single layer in the pan, with space in between them.
I often cook eggs in a 1-qt pan with a glass lid. I make sure the pan is hot enough that the egg sizzles continuously when I drop it in, and then leave the lid off just long enough to season the egg. Then I put on the lid, and wait for the white above the yolk to turn translucent (which I can see through the glass). At that point, the yolk is a little runny; shortly afterwards when the white it opaque, the yolk will be congealed on the outside but still a little runny on the inside, and not long after that, the yolk will be solid. Depending on what I'm in the mood for, I take it out at a different time.
The bottom of the egg is always browned, and the white is fluffy and full of holes like bread because of all the steam trapped inside. I'm not sure why your egg isn't turning out the way you like. It sounds like it might not have cooked fast enough on top, but the bottom got overcooked and over-hardened and dried out.
I'd suggest trying a few things:
- Don't check on the egg. Opening it up to check on it will let out all the steam. You might get a few wasted eggs at first while you get the hang of the timing, but it's not going to turn out right if you keep opening it up.
- Heat up the pan more before you start. You can always turn it down while it steams, but I find that cooking it when the butter just starts to sizzle isn't hot enough; I make sure it's hot enough to make the egg sizzle continuously once it hits the pan.
- Use a smaller pan. A big pan will take a while to fill with steam and heat all the way up.
Best Answer
I follow Alton Brown's recipe from Good Eats for grated (the only way!) hash browns and never have problems with it binding. It's from the episode "Another Man Food Show: Breakfast" if you want to search it out. He talks on the show about why the type of potato matters and recommends a high starch potato like an Idaho or Russet. I use Russets as they're readily available here and never have any issues.
Summary of the cooking process:
Notes: