Shells: May be made a day ahead.(short cut, use frozen phyllo cups) Heat oven to 375 degrees. Roll out pie dough and cut with 2” round cutter. Fit into gem pans and prick twice in the bottom of shell. Chill 20 minutes to firm dough.
Bake shells until golden brown, about 12-15 minutes, rotating once during baking. Remove baking sheets from oven; transfer to a wire rack.
Shallots : May be made a day or two ahead:.
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.
Creamy filling: May be made a day or two ahead:.
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.
To assemble and bake—Place shells on a cookie sheet.
Spoon or pipe 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.