Preheat broiler to medium. In a large oven-safe skillet over medium heat, melt butter. Add garlic and tomato paste, stirring constantly until tomato paste darkens and sticks to the pan, about 2-3 minutes. Add cherry tomatoes and season with oregano, salt, pepper, and a pinch of red pepper flakes. Cook until tomatoes start to burst, then add spinach and cook until slightly wilted.
Stir in broth, heavy cream, Parmesan, and herbs, bringing to a simmer. Reduce heat to low and simmer until sauce thickens slightly, about 3 minutes.
Meanwhile, bring a large pot of salted water to a boil. Add gnocchi and cook, stirring occasionally, until they float to the top, about 2 minutes.
Drain gnocchi, discarding pasta water, and add them to the sauce, tossing to coat. Top with mozzarella and broil until cheese is melted and bubbly, about 3-5 minutes.
Garnish with more herbs and serve hot. Enjoy your creamy gnocchi delight!