Crack 2 eggs into a bowl with 1 tablespoon of milk and a pinch of salt and pepper. Beat well with a fork until completely combined and a little frothy.
Melt half the butter in a non-stick frying pan over a medium heat until foaming but not brown.
Pour in the beaten eggs and let them set for 30 seconds, then draw a spatula around the edge of the pan, tilting it so the runny egg flows underneath. Repeat for 1 to 2 minutes until the top is nearly set.
Scatter half the ham and half the cheddar over one half of the omelette and let the cheese begin to melt, about 30 seconds.
Fold the empty half over the filling, slide the omelette onto a warm plate and keep warm while you repeat with the remaining ingredients.
Butter the toast and serve each omelette with a slice alongside.