Goat Cheese Tartlets with Caramelized Shallots

Combine the flour and salt in the bowl of a food processor; pulse for 5 seconds. Add the butter pieces, and process until the mixture resembles coarse meal. In a slow, steady stream, add 6 tablespoons of ice water through the feed tube. Pulse until the mixture holds together when squeezed. Divide dough into two equal balls. Flatten each ball into a disk, and cover with plastic wrap. Chill at least 1 hour. Set twelve 4-inch bottomless tartlet (flan) rings or twelve 4-inch tartlet pans with removable bottoms on two parchment-lined baking sheets. Lightly flour a clean working surface. Roll Pate Brisee to a 1/8-inch thickness. Cut out twelve 5-inch diameter circles, and fit into tartlet rings. Using a fork, prick pastry all over; chill until firm, at least 15 minutes. Heat oven to 375 degrees. Line shells with aluminum foil; fill with dry beans or pie weights. Transfer baking sheets to oven; bake shells 12 minutes, rotating once during baking. Remove beans and foil. Continue baking until slightly golden, 7 to 9 minutes. Remove baking sheets from oven; transfer to a wire rack. Reduce the oven temperature to 325 degrees. Melt butter in a medium skillet over medium-low heat. Add shallots and sugar; season with salt and pepper. Cook, stirring frequently, until shallots are very tender and have deeply caramelized, 30 to 35 minutes. Remove from heat; set aside. Place goat cheese in bowl of a food processor; puree until very smooth. Add heavy and sour creams; process until well combined. Transfer to a medium bowl. Stir in thyme and parsley; season with pepper. Spoon 2 to 3 tablespoons filling into each shell, filling to within 1/8-inch from top. Arrange 1 heaping teaspoon reserved shallots on top of each tartlet. Transfer baking sheets to oven; bake tartlets until filling has set, 13 to 15 minutes, rotating once. Transfer sheets to a wire rack to cool slightly, about 10 minutes. Remove rings. Sprinkle remaining parsley over tartlets. To serve, place tartlets on plates. Garnish each plate with frisee. Makes 12.