Heat two tablespoons oil in a large heavy pot over medium high. Add tomatoes, red pepper flakes, and a pinch of salt and cook tomatoes, undisturbed, about five minutes. Stir and continue to cook, scraping and stirring occasionally, until tomatoes are caramelized, five minutes more. Transfer tomatoes to a bowl.

Heat remaining tablespoon oil in the pot over medium heat and add onion and carrots. Cook until onions are soft and clear, about eight minutes. Add garlic and cook until fragrant, about one minute. Stir in tomato paste and cook one minute. Add reserved tomato juice, cooked tomatoes, and butternut squash. Scrape up any brown bits from the bottom of the pan. Add rosemary, thyme, bay leaf, beans, wine, and broth. Simmer partially covered for 15 minutes. Raise heat to medium, stir in kale and cook, covered five more minutes. Season with remaining 1/4 teaspoon salt, pepper, and parmesan cheese. Taste and adjust seasonings. Remove bay leaf. Divide among four bowls. Place one egg on top of each dish, if using. Serve with parmesan cheese on the side.