In a food processor, combine flour, salt, and cold unsalted butter, pulsing until the mixture resembles coarse crumbs. Gradually add cold water, mixing until the dough just holds together. On a floured surface, roll the dough thinly, then fit it into tartlet pans. Chill the pastry for at least 30 minutes.

Preheat your oven to 375°F (190°C). Line the chilled pastry with parchment paper, filling it with baking beans or weights. Bake for 15 minutes, then remove the parchment and weights. Bake for an additional 2 minutes to dry out the bottom crust; it should be lightly golden.

While the crust is baking, slice your onion thinly and heat 1 tablespoon of butter in a skillet over medium heat. Add the onions, along with a pinch of salt, sugar, and thyme. Cook for about 30 minutes until they become soft and deeply golden.

In a mixing bowl, whisk together the egg, heavy cream, and a pinch of salt and pepper. Once the onions are caramelized, layer them into the pre-baked tart crust, followed by crumbled goat cheese. Pour the egg and cream mixture evenly over the filling.

Place your filled tartlets back into the oven and bake for 20-25 minutes until the filling is set and slightly golden on top. Let the tartlets rest for a few minutes before serving.