Adjust rack to 6 to 8 inches below broiler element and preheat broiler to high. Heat butter in a 12-inch cast iron skillet or two 10-inch cast iron skillets over medium-high heat until foaming subsides and butter starts to brown. Add gnocchi in a single layer and toss to coat with browned butter. Cover with cheese, then transfer to broiler. Cook until puffed and golden brown, about 10 minutes. Sprinkle with herbs and serve.