How to Make It
Heat oven to 400° F. On a rimmed baking sheet, toss the potatoes with 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper. Roast, tossing once, until golden and tender, 30 to 35 minutes.
Meanwhile, in a large bowl, beat the eggs with ¼ teaspoon each salt and pepper. Heat the remaining tablespoon of oil in a medium cast-iron or some other ovenproof nonstick skillet over medium-high heat. Add the sausage and cook, breaking it up with a spoon, until browned and cooked through, 6 to 8 minutes.
Add the broccoli to the skillet and cook until softened, 3 to 4 minutes. Add the egg mixture and cook, stirring gently, until beginning to set, 1 to 2 minutes more.
Transfer the skillet to oven and bake until the frittata is set in the center, 8 to 12 minutes. Cut into wedges and serve with the potatoes.