Slice the onions lengthwise—from stem to root—to help them maintain their structure during caramelization.

If using homemade dough, roll it on a lightly floured surface into a 12-inch circle. Fit the dough into a 9 x 1 1/2-inch tart pan or a 9-inch pie dish, pressing it firmly into the corners. Extend the edges slightly higher than usual to account for shrinkage. Freeze the crust for 30 minutes.

Preheat the oven to 350°F (177°C). Line the chilled crust with aluminum foil, pressing it against the sides and leaving enough overhang for easy removal. Fill the crust at least two-thirds full with baking weights such as dried beans, rice, or pie weights.

Bake the crust for 15 minutes. Remove from the oven and allow it to cool briefly. Carefully remove the foil and the weights.

Prick the bottom of the crust with a fork to allow steam to escape. Return to the oven and bake for an additional 10 minutes or until lightly golden. Transfer to a wire rack to cool.

In a large heavy-bottomed sauté pan, heat the olive oil over medium heat. Add the sliced onions and a light sprinkle of salt. Cook, stirring occasionally, for 10 minutes until softened and translucent. Reduce heat to medium-low and cook for an additional 40 minutes, stirring occasionally, until deeply browned. Add the balsamic vinegar and cook for 10 minutes more, until fully caramelized. Remove from heat.

Place the tart pan on a baking sheet to catch any overflow. Sprinkle half of the Gruyère cheese evenly over the prepared crust. Spread the caramelized onions over the cheese, then top with the remaining cheese.

In a medium bowl, whisk together the milk, heavy cream, and eggs. Season with nutmeg, salt, and pepper. Pour the custard mixture over the onion and cheese layers.

Transfer the quiche to the 350°F oven and bake for 30–35 minutes, or until the center is just set. Cool on a wire rack for 10–15 minutes before slicing and serving.