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Thaw the pastry sheets at room temperature for 1 hour.
For tart shells, in a small bowl, mix egg yolk with water. Set aside. Unfold the pastry sheets on a lightly floured surface. Roll gently to flatten creases (you should have a 10-inch square). Cut 1/2-inch strips from all 4 sides of each pastry sheet. Brush the edges of the pastry sheets with the egg mixture. Place the cut strips on top and along edges of the pastry sheets, gently pressing in place to form a raised edge; trim ends. Place pastries on 2 parchment paper-lined baking sheets. Brush pastries with egg mixture. Prick pastry with a fork. Sprinkle with Asiago cheese. Bake, 1 sheet at a time, in a 425°F oven for 15 to 20 minutes or until puffed and golden brown. Cool on baking sheets on wire racks.
In a small bowl stir together goat cheese, garlic, and the thyme. Spread over bottom of tart shells.
Arrange tomato slices on top of the goat cheese mixture, overlapping slightly. Drizzle with 2 tablespoons olive oil. Sprinkle with basil and coarse salt, if you like. Slide onto cutting board or serving platter, cut each tart into serving-size pieces.