Heat the oven: Preheat to 375°F (190°C).
Place a rack in the center.
Prep the crust: Fit the chilled pie crust into a 9-inch pie plate. Crimp the edges. Prick the bottom with a fork a few times to release steam.
Blind bake: Line the crust with parchment.
Fill with pie weights or dried beans. Bake for 15 minutes. Remove weights and parchment; bake another 7–10 minutes, until the bottom looks dry and lightly golden.
Set aside to cool slightly. Reduce oven to 350°F (175°C).
Cook the bacon: Slice bacon into 1/2-inch pieces. Cook in a skillet over medium heat until crisp, 7–9 minutes.
Transfer to a paper towel–lined plate. Reserve 1 tablespoon of bacon fat in the pan; discard the rest.
Soften the shallot: Sauté minced shallot in the bacon fat over low heat for 2–3 minutes, until translucent and fragrant. Let cool a minute.
Whisk the custard: In a bowl, whisk eggs, heavy cream, and milk until smooth.
Stir in salt, pepper, and nutmeg. Avoid over-beating; you don’t want too much foam.
Layer the filling: Scatter the cooked bacon and shallot evenly over the crust. Add Gruyère and Parmesan in an even layer, reserving a tablespoon for the top.
Add the custard: Slowly pour the custard into the crust.
It should come near the top but not overflow. Sprinkle the reserved cheese over the surface.
Bake gently: Bake at 350°F (175°C) for 30–40 minutes, until the edges are set and the center wobbles slightly like Jell-O. If the crust browns too quickly, tent the edges with foil.
Rest and slice: Cool on a rack for 15–20 minutes.
The custard will finish setting. Garnish with chopped chives or parsley, then slice and serve warm or at room temperature.