Preheat oven to 400ºF (if you find that your crust is not browning fast enough, you can turn your heat up to 425ºF).
Melt butter in a medium saucepan over medium-low heat. Add onion and cook, stirring occasionally, until softened, about 4-5 minutes. Add garlic, curry powder, and salt and cook for 1 minute. Stir in cauliflower and peas and carrots. Sprinkle flour over the vegetables and stir to coat. Set aside 1 tablespoon cream (to brush the top of the pie with later), then stir in the remaining cream, along with broth, red pepper flakes, and chicken (or turkey)
Cook, stirring often, until the mixture begins to thicken, 3 to 5 minutes. Taste and adjust seasonings if needed. Transfer to a 9-inch deep-dish pie pan. Refrigerate, stirring occasionally, until cooled, about 10 minutes.
Once slightly cooled, spread the filling evenly. Lay the pie crust over it and crimp the edges with a fork. Use a sharp knife to make a few slits in the crust. Lightly and evenly brush with the reserved 1 tablespoon cream, avoiding the edges (they usually brown first). You don't have to use all the cream or the crust may get soggy.
Bake until the crust is light golden brown and the filling is bubbling, 30 to 40 minutes. This is a big range, but it all depends on your oven. If your oven is set at 425ºF, it might take 25-30 minutes instead. In either case, start checking for doneness starting from the 25 minute mark. You're looking for a firm flaky crust that is slightly golden brown and for the filling to be bubbling. Let cool for 5-10 minutes before slicing and serving.