Melt the butter in a small skillet over medium heat. When the butter begins to foam, add the onion and brown sugar and cook, stirring occasionally, until they are tender, about 8-10 minutes. Add the garlic and cook, stirring until fragrant, about 1 minute longer.
Meanwhile, preheat the oven to 375º F with a rack in the center position. Gently press the prepared pie dough into a 9-inch pie or quiche pan. Using a fork, poke holes all over the crust. Bake for 20 minutes. Remove from the oven and set aside.
In a large bowl, whisk the eggs, cream, salt, pepper, and nutmeg together until well combined. Stir in the cheese, bacon, and onion mixture. Pour the egg mixture into the prepared pie crust.
Bake until the eggs are set, about 35-40 minutes. The eggs should barely move when you jiggle the pan.
To serve, garnish with chives and cut into 8 wedges