Fill a large bowl with ice water. Bring about 1 inch of water to a boil in a large skillet.
Add the asparagus; cook until bright green and crisp-tender, 2 to 5 minutes, depending on the thickness of the asparagus.
Drain and transfer to the ice water to stop the cooking; drain and pat dry. Preheat the oven to 400 degrees F.
Roll out the puff pastry into a 10-by-16-inch rectangle on a floured surface.
Transfer to a parchment-lined baking sheet and prick all over with a fork.
Bake until light golden brown, about 12 minutes.
Let cool slightly on the baking sheet.
Meanwhile, mix the fontina, comte, shallot, egg yolks, milk, nutmeg and a pinch each of salt and pepper in a bowl until combined.
Spread the cheese mixture evenly over the puff pastry, leaving a 1-inch border on all sides. Toss the asparagus with the olive oil, 1/4 teaspoon salt, and pepper to taste. Arrange the asparagus on the tart and bake until the cheese mixture is slightly puffy, 15 to 20 minutes.