Heat a 10-inch cast-iron skillet over medium heat. Add the butter then the onion and garlic. Saute for 5 to 7 minutes. Add the ground beef and cook until browned. Stir in the tomato paste and stir to combine.
Add vegetable broth to the pan. Season with salt and pepper. Add pasta and bring to a boil, then simmer for 12 to 15 minutes, until the liquid is absorbed. Fold in half the cheese.
Place the spinach in between several paper towels and over the sink; squeeze to remove excess water. Stir in the spinach and sour cream and top with remaining cheese.
Turn on your broiler, place in the oven and broil until cheese is melted and bubbly.