To prepare the quiche liquid, crack the eggs into a bowl. Using a whisk, beat until light and blended. Add the milk, heavy cream, nutmeg, salt, and pepper. Whisk to blend. Cover and refrigerate while you prepare the filling. (You can prepare this a day or two in advance; just whisk the liquid again to blend the spices just before you use it.)
To prepare the filling, place the sliced tomatoes in a shallow bowl. Add the basil leaves. Drizzle the olive oil evenly over the tomatoes, then sprinkle lightly with sea salt and pepper. Toss gently to coat. Taste alittle piece of a tomato for seasonings.
To prepare the quiche, spray a cookie sheet with nonstick oil spray or line it with parchment paper to catch any drips. Set the prebaked piecrust on the prepared cookie sheet. Scatter the mozzarella cheese evenly in the crust, then scatter the feta cheese over the mozzarella cheese. Pick out the basil leaves and arrange them over the cheese about an inch and a half apart so that every slice will have a basil leaf, then arrange the tomatoes evenly in the piecrust over the cheeses, in a circular patter, overlapping slightly if needed. Whisk the quiche liquid, then slowly pour the liquid over the filling.
Using your fingers, rearrange the tomatoes that may have shifted, but don’t worry too much about them “floating” in the quiche liquid—the quiche will still be delicious if a bit uneven.
Bake the quiche in the preheated oven for 1 hour, until the top is golden brown and the center is just set. The quiche will be puffy when you first remove it from the oven, then it will flatten within 10 minutes or so—so don't get alarmed when it does. Let set for 15 minutes before cutting.
Serve hot or chilled. Refrigerate any leftovers for up to 2 days.