Roll out puff pastry into a 14-inch square on a lightly floured surface; cut into a 13-inch round with a paring knife (use a bowl or a plate as a template). Transfer to a 9-inch round baking dish or a 5 1/2-to-6-cup deep-dish pie plate. Prick all over with a fork. Freeze until firm, about 30 minutes.
Preheat oven to 350 degrees. Line tart shell with parchment and fill with pie weights or dried beans. Place on a baking sheet and bake until edges turn pale golden brown, about 40 minutes. Remove crust from oven and remove pie weights and parchment. Return crust to oven and bake until bottom is dry and golden brown, 5 to 10 minutes more. Let cool completely on a wire rack.
Bring a medium pot of water to a boil and add 2 tablespoons salt. Add asparagus stalks and cook until crisp-tender, about 2 minutes. Transfer to a bowl of ice water; when cool, transfer to a plate and pat dry. Add asparagus tips to boiling water and cook 30 seconds. Drain and transfer to ice water; drain when cool. Pat tips dry and toss with oil in a bowl. Transfer stalks to a blender. Add eggs, cream, flour, and 1 1/4 teaspoons salt to blender and puree until very smooth.
Pour custard into crust. Sprinkle with Gruyere and goat cheese and top with asparagus tips. Bake until edges of custard are puffed, top is golden brown, and center is set, about 40 minutes. (Tent with foil if necessary to prevent overbrowning.) Let cool on a wire rack 15 minutes before serving.
Crust can be blind-baked, cooled completely, and wrapped in plastic wrap 1 day ahead. Tart can be made 8 hours ahead and served at room temperature.