In a medium skillet, heat olive oil over medium heat. Add onions and salt. Cook onions, stirring occasionally, until they are golden brown, about 30 minutes. Add wine and cook for 2 minutes. Remove onions from heat and stir in pepper. Let cool slightly.
Place the tarts on a lined baking sheet. Sprinkle half of the cheese over the bottom of each tart shell. Spoon onions into the shell and spread evenly. Sprinkle thyme over the onions. Brush the exposed crust of each tartlet with the egg wash. Sprinkle with remaining cheese.
Bake in a preheated 375 F oven until the onions have turned a rich golden brown; about 20 minutes. Serve slightly warm or at room temperature garnished with thyme sprigs.