Preheat the oven to 350˚ with a rack in the middle. Butter a 9-inch pie dish and place dish on a baking sheet.

Heat 1 tablespoon butter and olive oil in a large skillet over medium-high heat. Add the onions with a pinch of salt and pepper; stir. Reduce the heat to medium, cover and cook, stirring occasionally, until soft and golden brown, about 15 minutes. Add the corn with another pinch of salt and pepper; cook, stirring, 1 minute. Taste and add more salt and pepper if needed. Transfer to a plate to cool slightly.

In a medium bowl, whisk together the eggs and half-and-half. Beat until frothy. Whisk in a grating of fresh nutmeg; season with salt and pepper.

Spread the onion and corn mixture in the bottom of the prepared pie dish. Sprinkle on ½ of the grated cheese. Pour the egg mixture over top. Bake 30 minutes, or until just set and very lightly golden around the edges. Let cool 10 minutes. Do Ahead: At this point, the quiche can be cooled completely then covered and refrigerated overnight. Bring to room temperature before proceeding.

Turn the oven to broil with a rack on top rung. Arrange the tomato slices on top of the tart, overlapping slightly. Sprinkle the remaining ½ cup of cheese over top. Broil 30-60 seconds, or until the cheese is just melted. Transfer to a cooling rack and let sit 5-10 minutes. Serve warm or at room temperature. Do Ahead: The tart can be made up to 2 hours in advance and left at room temperature.