Preheat the oven to 425°F (218°C).
Spread the tomato slices in a single layer on a rimmed baking sheet, being careful that the slices don't overlap. Drizzle the slices with enough oil to generously coat them, turning to slick both sides, and then sprinkle them with the basil, oregano, salt and pepper. Roast until the tomatoes start to shrink, 15 to 20 minutes. Let cool on the baking sheet for 30 minutes.
In a medium bowl, whisk the egg yolks until light and fluffy, and then whisk in the heavy cream.
Arrange half the roasted tomato slices in a single layer in the bottom of the pie crust. Sprinkle half of each cheese over the tomatoes. Repeat the layering of tomatoes and cheese and slowly pour the egg mixture over the top, letting it fill in all the nooks and crannies.
Bake the quiche until golden brown on top and set in the center, or until a toothpick inserted in the center comes out clean, 30 to 60 minutes, depending on the wateriness of your tomatoes and exactly how thick your pie plate is. Check on the quiche after 30 minutes and then again at 45 minutes and if the crust or the filling are sufficiently browned, loosely cover the quiche with foil until it finishes baking. Let the quiche rest at room temperature for 30 minutes before slicing it into wedges. The quiche is far more fabulous when served warm as opposed to cold. (Don't even think about serving leftovers straight from the fridge.)