Place the squash in the oven and roast for 40 minutes or until fork-tender. Scoop out the flesh and discard the skins. Transfer to a food processor and blitz until smooth.
Sauté shallots until slightly softened. Stir in the garlic, tomato paste, and chili flakes. Open the can of tomatoes. Crush each tomato before transferring it to the skillet.i
Pour in the vodka and add the basil and oregano sprigs and salt. Let simmer for 10-15 minutes or until the tomatoes have broken down.
Transfer the sauce to a food processor and blitz until smooth. Return it to the skillet and stir in the squash puree. Add the Parmigiano Reggiano and the cream.
Stir until the cheese melts and the cream is well integrated. Taste and season with salt accordingly.
Cook and drain the pasta and pour it into the skillet and toss to coat in the sauce.
Top pasta with torn fresh mozzarella and fresh basil leaves.