In a large bowl, whisk together flour and salt. Add cold, cubed butter and cut into the flour mixture using a pastry blender or your fingertips until it resembles coarse crumbs with some pea-sized pieces of butter remaining.

Gradually add ice water, 1 tablespoon at a time, mixing until the dough just comes together. Be careful not to overmix. Form the dough into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes (or up to 2 days).

In a large heavy-bottomed skillet, melt olive oil and butter over medium-low heat. Add the thinly sliced onions, sprinkle with 1/2 tsp salt and 1/4 tsp pepper.

Cook slowly, stirring occasionally, for 45-60 minutes, or until the onions are deeply golden brown, soft, and sweet. If they start to stick, add a tablespoon of water.

Stir in the brown sugar, balsamic vinegar, and chopped fresh thyme. Cook for another 5 minutes, allowing the liquid to evaporate and the flavors to meld. Remove from heat and let cool slightly.

Preheat oven to 375°F (190°C). Lightly grease a 12-cup standard muffin tin or tartlet pan.

On a lightly floured surface, roll out the chilled dough to about 1/8-inch thickness. Using a 3-inch round cutter (or a glass rim), cut out 12 circles. Carefully press each dough circle into the muffin tin cups.

Prick the bottoms of the pastry shells several times with a fork. Line each shell with a small piece of parchment paper and fill with pie weights or dried beans. Bake for 10-12 minutes, or until edges are lightly golden. Remove pie weights and parchment, then bake for another 3-5 minutes, or until the bottom is just set. Let cool slightly.

While the shells are blind baking, prepare the custard. In a medium bowl, whisk together eggs, heavy cream, nutmeg, 1/4 tsp salt, and 1/8 tsp pepper until well combined.

Divide the caramelized onions evenly among the pre-baked tartlet shells. Sprinkle a portion of the grated Gruyere cheese over the onions in each tartlet.

Carefully pour the egg custard mixture over the onions and cheese in each tartlet, filling almost to the top. Sprinkle with a little extra Gruyere cheese, if desired.

Return the tartlets to the oven (still at 375°F / 190°C). Bake for 20-25 minutes, or until the custard is set and lightly golden, and the cheese is bubbly.

Remove from oven and let cool in the muffin tin for 5-10 minutes before carefully removing. Garnish with fresh thyme sprigs, if desired. Serve warm or at room temperature.