In a small bowl, whisk together the broth, vinegar, maple syrup, and mustard. Set aside.
Heat the olive oil in a large skillet over medium-high heat. Add the gnocchi and cook for 5-7 minutes, stirring occasionally, until crispy and golden brown. Transfer to a plate.
Add the Brussels sprouts and shallots to the skillet and cook for 3-4 minutes, until starting to soften. Add the sausage and cook, breaking it up with a wooden spoon, for 4-5 minutes until cooked through.
Pour the broth mixture into the skillet and bring to a simmer. Cook for 2-3 minutes, until slightly thickened. Add the gnocchi back to the skillet and toss to coat. Sprinkle with the rosemary and Parmigiano-Reggiano cheese before serving.
