Caramelised onion frittata

3 medium sized brown onions - sliced, not diced
1 tbsp butter
1 tbsp olive oil
8 eggs
2-3 tbsp pesto (any kind you like)
salt/pepper
3/4 cup milk
1/2 cup thinly sliced or grated cheddar cheese

Melt the butter and olive oil in a frying pan (about 25 cm diameter) on low heat. Once melted, add the onions and cook for 10-15 min, stirring occasionally, until the onions turn golden.
Meanwhile, whisk together the eggs, milk, salt and pepper, and pesto in a large bowl. Once the onions are cooked, pour the egg mixture on top of the onions, and sprinkle the cheese on top. Allow to cook on low heat for ~6 min, or until eggs have almost set in the frying pan.
Place the frying pan under a hot grill (broiler, they call it in Canada) for 1-2 min until eggs have competely set and cheese has melted/browned.