Melt butter in a 12-inch skillet over medium-high heat. Add gnocchi in a single layer and cook on one side for 2-3 minutes until browned and toasted. Flip and repeat. Remove gnocchi to a plate and set aside.
Turn the heat to high and return the skillet to stove. After pan is very hot and smoking, add the beef and season with salt, pepper, cumin, paprika, and mustard powder. Add onion and garlic and cook, stirring occasionally, until beef is browned and onions are golden. Drain if necessary.
Add the tomatoes, broth, and gnocchi back to the skillet. Stir to combine. Bring to a boil, then cover, reduce heat to medium-low and simmer for 5 minutes until gnocchi is tender and liquid is mostly absorbed.
Take off the heat and add cream cheese and ½ cup of cheese, stir to combine. Top with remaining cheese and green onions. Broil in the oven until bubbly, about 3 minutes.