In a Dutch oven, heat the pork fat and 2 tablespoons of the olive oil over high heat until almost smoking. Add the parsley and onion and cook, stirring, until the onion is browned and soft, 8 to 10 minutes.
Stir in the tomato paste, reduce the heat to medium, and cook for 10 minutes. Add the chicken stock and beans and bring to a boil. Lower the heat and simmer for 30 minutes.
Add the pasta and simmer for 10 more minutes. Remove from the heat, season with salt and pepper, and allow to rest for 10 minutes.
Divide the soup among six serving bowls, drizzle with the remaining ¼ cup olive oil, and serve.