Melt the butter in a large skillet over medium-low heat. Toss in the celery, leeks, carrots, and red bell pepper. Cook, stirring, for about 10 minutes, or until they are tender.
Season with salt and pepper, then place the vegetables into a bowl and let cool.
Preheat the oven to 400 degrees. Put the crust on a baking sheet lined with parchment paper.
Spoon the vegetables into the tart shell and spread them out evenly.
Whisk the cream, egg, and egg yolk together, season with salt and pepper, and carefully pour over the vegetables. You may have too much custard, so wait for it to settle and add just enough so your tart shell does not overflow.
Carefully place the baking sheet into the oven.
Bake for 20 minutes. Sprinkle the cheese over the top and bake for another 5 to 10 minutes, or until the cheese is light brown and the center is puffed and set.
Let cool on a wire rack before serving.
