Par-bake the crust. Preheat the oven to 375ºF. While the oven is heating, put the pie crust in its tin on the counter and let it thaw slightly, so you can prick it all over with a fork. Line the pie shell with foil or parchment paper, then weight it with dried beans or pie weights. Bake the crust until slightly golden on the edges, about 15 to 20 minutes. Transfer to a cooling rack and remove weights, simply picking the foil or parchment at the corners.
Meanwhile, make the filling. Bring a pot of water to boil. Rinse the broccoli rabe and working one stem at a time, cut off much of the thick stem and chop the leaves, buds and a portion of the stem crosswise. You want a generous two cups of tightly packed pieces—it will cook down. Blanch the chopped broccoli rabe in the boiling water for 2 minutes, then drain in a colander and rinse under cold running water. Drain on a paper towel-lined plate, gently squeezing out excess water.
Heat a large, deep sauté pan over medium flame. Add enough oil to coat the bottom, about 2 tablespoons. If you’re working with uncooked chicken, add it to the pan, season lightly with salt and cook, stirring frequently, until there’s no pink on the outside; you don’t need to brown it or even cook it completely through. If you’re using cooked rotisserie chicken, add it to the pan, but don’t salt it. Toss to coat with oil. Add the broccoli rabe and garlic, and cook, stirring frequently to combine everything, for about 2 minutes. Remove from heat and stir in lemon juice.
Using a slotted spoon, transfer the mixture to a paper towel-lined plate and let it cool slightly, then top with another paper towel and gently press down to squeeze moisture from it.
Beat eggs in a bowl, then add half & half and beat to combine.
Assemble and bake the quiche. Spread the Dijon mustard in the bottom of the crust (this is optional, but the mustard sharpens the cheese flavors without imparting its own taste). Put broccoli rabe/chicken mixture into the crust and gently spread with a fork to evenly distribute it. Sprinkle cheese evenly over the filling. Pour the egg mixture over the top, using your fork to gently help it settle in around the filling.
Transfer to the middle rack of the oven and bake the quiche until it has puffed up and is set and beautifully browned, about 25 to 35 minutes. You can test with a sharp knife to make sure the middle is set.
Cool on a rack at least 10 minutes, then serve. You can also serve it room temperature, but I think warm is best. See Kitchen Notes about reheating leftovers.