Preheat oven to 400°. Place potatoes, broccoli, bell pepper, and red onion on a large sheet tray. Drizzle with oil and season with garlic powder, oregano, mustard, salt, pepper, and large pinch of red pepper flakes. Toss to coat all the veggies, then spread out into an even layer.
Bake for 25 minutes. Remove tray from oven and add sausage. Toss veggies with sausage then spread back out into an even layer.
Bake again until sausage has darkened and is warmed through and veggies are crisp tender, another 20 to 25 minutes more.
