Add the oil to the pan over medium heat and heat for 1 minute before adding the onion. Cook the onion for 2 to 3 minutes until translucent before adding the red pepper. Saute the onion and pepper together for 1 minute, add the mushrooms and then cook together for 2 minutes. Add the peas and tomatoes, season all the vegetables with salt and pepper and continue to cook for 5 minutes.
Break the eggs into a large bowl and whip together with a whisk until smooth, add the milk and herbs, pour over the vegetables cooking in the pan. Stir for 1 to 2 minutes to blend all of the ingredients thoroughly and begin cooking the eggs. Reduce the heat to low, add the cheese, place a cover on the pan and allow the frittata to cook until the eggs are fully set but not overcooked (check to see that the bottom does not burn by gently lifting with a fork).
The frittata is now cooked completely and the top can be browned under a broiler or the whole frittata may be inverted onto a serving dish so that the nicely browned bottom becomes the top that is seen when served