Heat avocado oil in a large pot or Dutch oven over medium heat. Add the ground beef and cook, breaking it into small crumbles, until browned and cooked through. Remove from the pot and set aside.
Add a little more oil if needed, then stir in the diced onion. Cook for about 5 minutes, until softened and translucent. Add the garlic and cook for 1–2 minutes until fragrant.
Stir in the tomato paste and Italian seasoning, cooking for another 2 minutes to deepen the flavor.
Pour in the chicken broth and crushed tomatoes, stirring to combine. Return the cooked beef to the pot, cover, and bring to a simmer. Reduce heat and let simmer for 10 minutes.
Uncover and add the drained beans and gnocchi. Stir and cook for about 2 minutes, just until the gnocchi are tender.
Reduce heat to medium-low and stir in the spinach (if using), salt, and black pepper. Cook until the spinach is wilted.
Pour in the heavy cream and gently stir. Let the soup simmer for a few more minutes until slightly thickened.
Ladle into bowls and top with freshly grated parmesan cheese before serving.