In a large saucepan, heat the olive oil and butter over medium heat until the butter begins to foam slightly. Add the chopped pancetta and cook for a few minutes, stirring occasionally, until it turns golden and releases its flavor. Stir in the onion, sage, and parsley, and sauté gently for about 5 minutes, allowing the onion to soften and become fragrant.

Add the chopped garlic, carrots, celery, and potatoes. Continue cooking for another 2 minutes, stirring frequently to coat the vegetables in the flavorful fat. Add the green beans and courgettes, and cook for an additional couple of minutes until they start to soften slightly.

Pour in about 2.5 liters of hot water, ensuring the vegetables are well covered. Stir in the canned plum tomatoes along with their juice, season with salt and pepper to taste, and bring the mixture to a gentle simmer. Cover the pan and let the soup cook over very low heat for at least 1 hour, allowing the flavors to deepen and meld together beautifully.

After the long simmer, add the rice and drained borlotti beans to the pot. Stir well, and continue cooking uncovered over a steady simmer until the rice becomes al dente — tender but still slightly firm to the bite. Adjust the seasoning if needed.

Serve the minestrone hot, either with freshly grated Parmesan cheese stirred directly into the pot for a richer texture, or provide a bowl of Parmesan on the side for each guest to sprinkle as they wish. This hearty, rustic soup captures the comforting essence of Italian home cooking in every spoonful.