Preheat the oven to 400°.

Tart Dough: Combine the flour and salt in the bowl of a food processor. Pulse briefly. Add the butter and pulse approximately 30 times until the butter is the size of grains of barley. Dump the mixture into a large bowl. Add a few tablespoons of ice water and using your hand like a claw, mix the dough together. Keep adding ice water as necessary, being careful to not add to much. You want a dough that just comes together with pressure, not a wet, sticky clump.

Lay a sheet of plastic wrap on the counter and pour out the dough onto it. Bringing up the sides of the plastic wrap, form the dough into a ball and then press out into a disc shape. You can roll it out now or if it seems warm in your kitchen, cover the dough completely with wrap and place in the refrigerator to chill for 15 minutes.

Filling: If you are using dried morels, pour boiling water over them and rehydrate for 15 minutes until soft. Slice thin. If you are using fresh morels, brush off any surface dirt and slice them into rings. Heat the olive oil in a sauté pan over medium high heat. Add the leeks and sauté for about 2–3 minutes until tender. Add a bit of vermouth it it gets too dry. Add the mushrooms and thyme and sauté for five minutes. Season the vegetables lightly with salt and pepper. Let the mixture cool.

Assembly: Lightly dust the countertop with flour. With a rolling pin, roll dough out to a large circle that is a scant ¹/₄" thick. (Rough edges are fine, because you will fold this tart into a very rustic shape.) Leaving a 1 ¹/₂" border all round, spread the cheese mixture all around the bottom of the tart. Spread the mushroom/leek mixture on top and then top with the grated gruyere cheese.Fold the edges over onto itself at 2-inch intervals. Brush the edges with the reserved beaten egg. Bake for 30 minutes or until golden brown on the edges and the cheese has melted nicely on top. Serve right away.

For some added color and interest you can serve a slice of tart on a small arugula salad.