Trim and halve the Brussels sprouts.
Using a vegetable peeler, peel thick strips of lemon zest, then coarsely chop. (You should have about 2 teaspoons chopped zest.)
In a large (preferably 12-inch) skillet, heat 2 tablespoons olive oil over medium-high.
Add the brussels sprouts, season with ½ teaspoon salt and a few grinds of pepper, then arrange the brussels sprouts in an even layer, cut-side down.
Scatter the lemon zest over the top and cook, undisturbed, until the Brussels sprouts are well browned underneath, 3 to 5 minutes.
Add the red-pepper flakes, stir and cook until the brussels sprouts are crisp-tender, 2 to 3 minutes.
Transfer to a medium bowl.
In the same skillet, heat the remaining 1 tablespoon olive oil over medium-high.
Break up any gnocchi that are stuck together, add them to the pan and cook, over medium flame, covered and undisturbed, until golden brown on one side, 2 to 4 minutes.
Add the butter and balsamic, season with salt and a generous amount of black pepper, and cook, stirring, until the butter is golden, nutty smelling and foaming, 1 to 2 minutes.
Stir in the Brussels sprouts until warmed through. Serve with grated Parmesan.
