Preheat the oven to 400F. Line a baking sheet with parchment paper or spray with a nonstick spray.
In a bowl, combine gnocchi with 1 tablespoon olive oil, garlic powder, and salt. Toss well and break up the larger clumps. Spread on a baking sheet in an even layer.
Add sausages next to gnocchi. Then place a wire rack on top of the baking sheet.
In a bowl, combine broccoli with 1 tablespoon oil, salt, and Parmesan cheese. Toss well and spread on the wire rack.
In a bowl, combine zucchini with 1 tablespoon oil, salt, and lemon. Toss well and add to the wire rack.
In a bowl, combine shishito peppers with 1 tablespoon oil and salt. Toss well and add to the wire rack.
Bake in the oven for 15 minutes. Remove the wire rack and transfer the vegetables to a plate. Flip the gnocchi and sausages, then roast for 5 minutes. Remove from the oven and sprinkle more Parmesan cheese on top.