Heat oven to 425 °F. Line a large rimmed sheet pan with parchment.
In a large bowl, toss the gnocchi, sausage, broccoli, olive oil, salt, black pepper, and red pepper flakes until evenly coated. Spread in a single layer on the prepared pan.
Roast 12 minutes. Remove the pan, scatter the garlic over the top, stir gently, and spread back into a single layer.
Roast 10-13 minutes more, until the gnocchi are golden and crisp at the edges, the broccoli is tender-crisp, and the sausage is cooked through (165 °F).
Drizzle with lemon juice, sprinkle with Parmesan, and serve hot.