Preheat the oven to 400F. Cover a half sheet tray with a piece of parchment paper and set aside.
Roll out the dough so it's circular in shape, dusting with flour to prevent sticking as needed. Transfer to the sheet tray and set aside.
Using a spoon, whip the goat cheese to make it spreadable. Spread it over the center of the galette.
Add the broccolini florets and leaves and the lemon slices to a bowl. Sprinkle with olive oil, then season with crushed red pepper, salt, and pepper to taste.
Arrange the broccolini and lemon slices on top of the goat cheese, leaving a 2 inch rim of pie crust around the sides.
Fold up the edges towards the center and crimp with a fork.
Bake for 20-25 minutes, until crust is browned and fragrant and lemons and broccolini are charred.