Melt butter in large saucepan over medium heat. Add onions, thyme sprigs, and 1/2 teaspoon salt, stirring to mix. Cover and reduce heat to low. Cook, stirring occasionally, until dark golden brown, about 45 minutes. Remove thyme stems.
Meanwhile, preheat oven to 450° F. Toss butternut squash with olive oil and 1/2 teaspoon salt and spread out on baking sheet.
Bake until browned and very soft, stirring once, about 40 minutes.
Reduce oven heat to 350° F. Roll dough out until thin and press into a well-greased 10-inch tart pan. Prick all over with a fork and bake in oven 10 minutes.
In a medium mixing bowl, combine eggs, crème fraîche, gruyère, Parmesan, and black pepper.
Spread caramelized onions in bottom of tart and top with butternut squash. Pour gruyère mixture over the squash, making sure to spread it evenly throughout the tart.
Bake until golden brown and cooked through, about 30 to 40 minutes.