Preheat oven to 180C/350F.
Heat the oil in a frying pan over a medium heat. Add the onions and cook for 3 or 4 minutes until starting to soften.
Add the broccoli and cook for a further 4 or 5 minutes until that is starting to soften too.
Add the peas and cook for a further 3 minutes.
Put the vegetables into a shallow dish and pour over the beaten eggs.
Sprinkle over the cheese and plenty of salt and freshly ground black pepper.
Bake for 25-30 minutes until the quiche is cooked through but is still a little wobbly.
Leave to cool for 5 minutes before slicing.
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