Preheat oven to 350˚F.
In a medium sized baking tin, toss together the red onion, garlic, cherry tomatoes, olive oil, salt and pepper. Roast in the oven for 15-20 minutes or until the vegetables have softened and colored a bit. Set aside.
Cook the gnocchi according to package directions. While the gnocchi is boiling, heat a large skillet over medium-high heat and melt the butter. Once the gnocchi are cooked and floating at the surface of your pot, transfer to your skillet using a slotted spoon. Do not throw out the cooking liquid from the gnocchi.
Arrange the gnocchi so they are in one layer in the skillet. You may have to do this in batches. Leave for a few minutes or until golden brown on the bottom. Squeeze in the juice from half a lemon. Toss and color on the other side. Transfer the colored gnocchi to a bowl and set aside. Add about 1/2 cup of the cooking water to the skillet along with 1/2 of the parmesan. Bring to a simmer. Add the roasted vegetables and capers (if using). Combine well and then add back the gnocchi. Toss carefully so all the gnocchi are coated in the sauce. Add more salt or pepper if desired. Remove from the heat and stir in the arugula. Serve topped with the remaining parmesan.