Heat oven to 425°F. Toss squash with olive oil, 1/4 tsp salt, and black pepper. Spread on a sheet pan.
Roast squash 20–25 minutes, stirring once, until tender and lightly caramelized. Set aside to cool briefly.
Lower oven to 375°F. Fit crust into a 9-inch pie plate and crimp edges. Line with parchment and weights; bake 10 minutes.
Remove parchment and weights. Bake crust 5 more minutes until lightly golden. Let cool while you prep the filling.
Melt butter in a skillet over medium heat. Soften onion for 5 minutes. Stir in garlic for 30 seconds. Cool slightly.
Whisk eggs, half-and-half, milk, remaining 3/4 tsp salt, nutmeg, and thyme in a bowl until smooth.
Scatter half the cheese into the crust. Add roasted squash and onion mixture. Pour in the custard. Top with remaining cheese.
Bake 35–40 minutes at 375°F until the center is just set and the top is lightly browned. Tent if browning fast.
Rest 10 minutes before slicing. Serve warm or at room temperature.