Preheat the oven to 375°F.
Place the pie crust on a baking sheet and allow to thaw for 10 minutes. Prick all over with a fork and bake for 10 minutes. If the pie crust still puffs up in any spot, gently press it back down into place with the back of the fork.
In a medium bowl, whisk together the eggs, heavy cream, thyme, onion powder, garlic powder, pepper, and salt if using. Set aside.
Keep the pie crust on the baking sheet. Place half of the cheese into the pie crust, add the ham on top, add the broccoli, and the remaining cheese. Slowly pour the egg mixture into the pie, you need to do this slowly so it does not overflow.
Bake for 35-40 minutes, the center might be the slightest bit jiggly. To check your quiche for doneness, you can use a butter knife inserted into the center. If there is any milky liquid on the knife, it needs another few minutes.
Let cool for 15 minutes to set. Serve with a garnish of scallions, optional.