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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.
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Preheat the oven to 375°F /190°C.
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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.
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Cut the mint leaves with a sharp knife into thin strips. Toss half of it in a bowl with the peas.
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Whisk together the milk, half and half, eggs, egg whites, salt, and pepper.
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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.
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Bake for about 40 minutes, or until lightly golden and set. Remove, cool slightly, and serve.