Caramelized Onion and Carrot Tart

**Make the crust:** In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together. Form the dough into a disc, wrap it in plastic wrap, and chill in the refrigerator for at least 30 minutes.

Preheat oven to 400°F (200°C).

On a lightly floured surface, roll out the dough into a 12-inch circle. Transfer the dough to a 9-inch tart pan with a removable bottom, pressing it into the bottom and up the sides. Trim any excess dough and crimp the edges. Prick the bottom of the crust with a fork.

Blind bake the crust: Line the crust with parchment paper and fill it with pie weights or dried beans. Bake for 15 minutes. Remove the parchment paper and weights, and bake for another 5-7 minutes, or until lightly golden.

**Prepare the caramelized onions and carrots:** While the crust is baking, heat olive oil in a large skillet over medium-low heat. Add the sliced onions and carrots. Cook, stirring occasionally, until they are softened and deeply caramelized, about 25-30 minutes. This takes time, so be patient and don't rush the process.

Stir in the chopped thyme, balsamic vinegar, brown sugar, salt, and pepper. Cook for another 2-3 minutes, until the balsamic vinegar has reduced slightly.

Remove the tart crust from the oven. If using Gruyere cheese, sprinkle it evenly over the bottom of the crust.

Spread the caramelized onion and carrot mixture evenly over the crust.

Bake for 10-15 minutes, or until the filling is heated through and the crust is golden brown.

Let the tart cool slightly before slicing and serving.