Cook gnocchi in a large Dutch oven according to package directions. Drain and set aside. Add the broccoli and cook 1 minute, then drain.
While the gnocchi and broccoli cook, heat the large skillet over medium heat. Add the butter and oil, and cook until the butter browns, about 7 minutes. Watch carefully and don't let it burn. Add the chopped sage and stir for 1 more minute. Add the gnocchi and broccoli and pepper to the pan, then toss to coat. Serve with the toasted almonds and Romano cheese.