Dice the peppers and zucchini.
Beat the eggs with a pinch of salt and add the heavy cream (or plain yogurt).
In a 10-inch cast iron pan (or ovenproof pan), heat the 2 tbsp of oil over medium-high heat.
Add the diced peppers and fry for about 5 minutes until slightly charred/browned on the outside. Stir occasionally.
Add the zucchini, remaining salt, and pepper and fry medium-high for another 4-5 minutes.
Turn the heat down to medium, and cook for another 10 minutes, stirring occasionally, until the veggies are fully cooked. Cover them with a lid if you want to speed up the process.
Add 1 tbsp of butter and stir it into the veggies until melted (about 30 seconds).
Add the beaten eggs.
Add the goat’s cheese, the parmesan, and (optionally) chopped parsley.
Bake in the preheated oven at 390°F (200°C) until cooked through, golden, and puffed up, about 15-18 minutes.