Prepare the Soffrito: In a large pot over medium heat, pour a generous amount of extra virgin olive oil. Add diced celery, onion, and carrots. Add leaves from a sprig of rosemary. Stir to combine.
Cook the Soffrito: Add a splash of water to prevent burning. Cover with a lid and cook for 10 minutes.
Add Pumpkin and Potatoes: Add sliced pumpkin and diced potatoes to the pot. Drizzle with more olive oil and stir. Add water to cover the ingredients. Cover and cook for 10-15 minutes.
Add Tomatoes and Broccoli: Add diced tomatoes and sliced broccoli to the pot. Add the Parmigiano rind and another sprig of rosemary. Season with salt and pepper. Add water if needed to cover the ingredients. Cover and cook for 10 minutes.
Add Beans, Lentils, and Parsley: Stir in mixed beans, lentils, and a handful of chopped parsley. Add water if needed. Cover and cook on medium-high heat for 20 minutes, stirring occasionally.
Cook the Pasta: Add Ditalini pasta to the pot and cook for 2-3 minutes less than the package instructions suggest. Stir to prevent sticking.
Final Cooking: Let the soup cook uncovered for an additional 10 minutes, stirring occasionally. Check for doneness and seasoning, adjusting as needed.
Serve: Remove the pot from the heat and serve the minestrone soup immediately.