Make the crust: In a food processor, combine the flour and salt. Add the cold butter and pulse until the mixture resembles coarse crumbs. Gradually add the ice water, 1 tablespoon at a time, pulsing until the dough begins to come together. Turn the dough out onto a floured surface and form it into a disk. Wrap it in plastic wrap and refrigerate for at least 30 minutes.

Preheat the oven: Preheat your oven to 375°F (190°C).

Roast the vegetables: In a large pan, heat olive oil over medium heat. Add the grated carrots and sliced onions, and season with salt and pepper. Sauté for about 5-7 minutes, until they start to soften. Transfer the mixture to a baking sheet and roast in the oven for 10-15 minutes, or until tender and lightly caramelized. Remove from the oven and set aside.

Prepare the crust: Roll out the chilled dough on a floured surface to fit into a 9-inch pie pan. Gently press it into the pan, trimming any excess dough. Prick the bottom of the crust with a fork and bake for 10-12 minutes until slightly golden. Remove from the oven and set aside.

Prepare the filling: In a large bowl, whisk together the eggs, heavy cream, milk, nutmeg, salt, and pepper. Stir in the roasted carrot-onion mixture and shredded cheddar cheese. Add fresh thyme if using.

Assemble the quiche: Pour the egg mixture into the prepared crust, spreading the vegetables and cheese evenly. Bake for 30-35 minutes, or until the quiche is set in the center and lightly golden on top.

Cool and serve: Let the quiche cool for about 10 minutes before slicing. Serve warm or at room temperature.