Render the bacon. Heat the olive oil in a 4-5 qt dutch oven over medium heat. Once the oil is hot, add the bacon and cook for 6-8 minutes, stirring often, until the bacon is crispy. Use a slotted spoon to transfer the bacon to a small bowl. Discard all but 1 tablespoon of bacon fat.
Saute the veggies. Lower the heat slightly and add the butter. Once it’s melted and foamy, add the onions, carrot, and fennel to the pot and saute for 5-6 minutes, until the vegetables are soft. Stir in the dried oregano, basil, red pepper flakes, and garlic and cook for another minute. Stir in the tomato paste and cook for another 2-3 minutes, until the tomato paste has darkened in color.
Simmer the soup. Pour in the chicken stock and bring to a gentle simmer for 10-15 minutes, just until the liquid has reduced slightly. Stir in the gnocchi and bacon and cover. Simmer for 5-7 minutes, until the gnocchi is tender.
Finish the gnocchi soup. Pour in the heavy cream and add the chopped kale and basil leaves. Simmer for another 2-3 minutes, until the kale is tender. Stir well and season to taste with salt and pepper. Ladle the soup into bowls and top with parmesan, basil, and a drizzle of olive oil.