Combine the flour, salt, pepper, and baking powder in the bowl of a food processor and pulse on and off a few times to combine. Add the olive oil and ice water and pulse until a dough mass forms. Remove it and knead it lightly on a floured surface. When it’s smooth, after about 6 – 8 minutes, shape it into a flat disk, wrap it in plastic wrap and chill it for about 20 minutes, or up to two days. Remove when ready to use.
Preheat the oven to 375°F /190°C.
Lightly oil a 10- or 12-inch round ovenproof baking dish. Roll out the dough on a floured surface to a circle about two inches larger than the circumference of your baking dish. Chill until ready to use.
Cut the mint leaves with a sharp knife into thin strips. Toss half of it in a bowl with the peas.
Whisk together the milk, half and half, eggs, egg whites, salt, and pepper.
Strew half the feta over the bottom of the quiche pastry. Spread the peas over the feta. Pour over the milk-egg mixture and top with the remaining cheese.
Bake for about 40 minutes, or until lightly golden and set. Remove, cool slightly, and serve.