Preheat oven to 425ºF. Spread eggplant on a rimmed baking sheet, and toss with 2 Tbsp. oil and 1/2 tsp. salt. Bake for 25 to 27 minutes, tossing once halfway through, until soft.
Meanwhile, heat remaining 2 Tbsp. oil in a Dutch oven or large soup pot over medium-high heat. Once hot, add the onion, and cook 6 to 7 minutes, until soft. Stir in the garlic, tomato paste, oregano, fennel seeds, and red pepper flakes. Cook for 4 to 5 minutes, until the tomato paste turns brick red.
Add the beans, kale, tomato puree, vegetable broth, water, black pepper, and remaining 1 tsp salt; stir well until everything is combined. Bring the mixture to a boil. Once the soup is boiling, add the roasted eggplant and pasta. Reduce heat and simmer, uncovered, for 12 to 15 minutes, or until the pasta is al dente.
Gradually sprinkle in the Parmesan cheese while stirring continuously. (Adding it all at once could result in clumping.) Once the cheese is combined, stir in the heavy cream, taste and adjust seasonings as needed, and serve.