Preheat the oven to 400 degrees F. Unroll the pie crust and fit it into a 9-inch deep-dish pie plate.
Arrange 6 strips of the bacon one above the other in a square on a baking sheet; the edges should touch but not overlap. Working with one of the remaining strips at a time, weave them over and under to form a lattice.
Whisk the Cheddar, milk, eggs, broccoli, 1 teaspoon salt and a few grinds of pepper in a medium bowl until well combined. Pour into the pie crust. Bake the bacon lattice and quiche on separate baking sheets until the bacon is just starting to crisp up and the quiche is slightly set but still jiggly in the center, about 15 minutes.
Use 2 spatulas to transfer the bacon lattice to the top of the quiche. Continue baking until the bacon is golden brown and crisp and the quiche is set, 15 to 20 minutes more. Let stand for 10 minutes before serving.
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