Preheat your oven to 400°F (200°C). On a large baking sheet, toss the diced butternut squash, Brussels sprouts, and carrots with olive oil, 1/4 tsp salt, and 1/8 tsp pepper. Roast for 20-25 minutes until tender and lightly caramelized.

While vegetables roast, heat a small skillet over medium heat. Add the chopped onion and cook until softened, about 5-7 minutes. Add the minced garlic and cook for one more minute until fragrant. Set aside.

Reduce oven temperature to 375°F (190°C). Press the pie crust into a 9-inch pie plate. Line the crust with parchment paper, fill with pie weights, and blind bake for 15 minutes. Remove the weights and parchment, then bake for another 5-7 minutes until the bottom is lightly golden.

Layer the ingredients in the pre-baked crust: start with the cooked onions and garlic, followed by the roasted vegetables, and finally the shredded Gruyère cheese.

In a medium bowl, whisk together the eggs, heavy cream, milk, remaining 1/4 tsp salt, 1/8 tsp pepper, and the nutmeg until fully combined and smooth.

Carefully pour the egg mixture over the vegetables and cheese in the crust.

Bake for 35-45 minutes, or until the center is just set (it should wobble slightly). The edges should be golden brown. Let the quiche cool on a wire rack for at least 15 minutes before slicing and serving to allow the custard to set fully.