I would do it the other way round, I'd fry the sausages first, then add the veg. This has a few benefits as I see it:-
- The sausages will brown more evenly, purely aesthetic but some people will think they are not cooked if they are not brown.
- You'll get the oil out of the sausages so you'll have a better idea of how much oil to add when you add the veg, if any.
- The veg will sweat down in the sausage oil which is likely to be much nicer than the other oil
- You can cook the sausages on a really low heat to start with so that they really get sticky and caramelised, then when you add the veg back in you can add a spoon of water/vinegar/stock to deglaze the pan an get that lovely sticky sausage goodness all over your veggies, which will be delicious.
You could optionally take the cooked sausages out of the pan and do the veg separately, or keep 'em in there, I'd probably take them out so I could turn the heat up a bit without having to worry about the sausages.
I'd say that when you do add the veg you want a thin (1mm ish) layer of oil in the pan. Depending on the pan this is probably a tables spoon or 2. You probably don't need to scale up as if you are cooking a bigger batch you will probably use a bigger pan, and so a similar depth of oil should suffice. If you are using the same pan, but with a deeper amount of veg, then I would add a little more, but I would make the depth of oil in the pan proportional to the depth of veggies.
Remember the golden rule. You can always add, you can never take away. And once the veg start to cook down and the volume decreases then the oil ratio will be higher, so start out with a little less than you think, just enough to coat the veg when tossed in it.
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.
Best Answer
Stirring and scraping would prevent burned bits. The onions and peppers release water as they cook the mechanical action of stirring and scraping pulls up the brown bits before they burn and incorporates them into the peppers and onions.