When writers state the utensils we need for a recipe, we use whatever we have that most closely follows the specification. But it is an obvious point that the equipment will have a big influence on the quality of the dish.
Take this six-egg cheese omelette - a frittata I suppose you'd call it, because of its size, and the slow cooking. I made it in a 20cm pan. That seems much too small. But I liked the cake-like texture; and, strangely, the base of the omelette was not overcooked, despite the lengthier cooking time that the small pan required.
It helps if the pan has an effective non-stick surface. You can stir the eggs for a while, rather as if you're scrambling them, before allowing the omelette to set.
I used 80g of Cheddar cheese, grated.
Lightly beat the eggs. Add salt.
Melt a knob (large walnut-sized) of butter in the frying pan, over a low heat. Pour in the eggs. Stir them around from time to time, until they are starting to set properly.
When about two thirds of the egg is set, but the omelette is still runny on the surface, scatter over the cheese. Place the pan on the rack below your overhead grill, set at its lowest. Remove as soon as the omelette starts to look solid - the fierce heat of the grill can easily overcook it.