Preheat the oven to 200°C (400°F) and line a baking sheet with parchment paper. Halve the honeynut squash lengthwise and scoop out the seeds. Place on the sheet, coat with 1 tbsp olive oil, season with salt and turn cut-side down. Bake until completely tender, about 30 minutes. Let cool, then scoop out the flesh and mash. In a large saucepan, heat the remaining olive oil and the butter. Add the peppers and shallot and cook over medium heat until soft and beginning to caramelize, 7 to 8 minutes. Add the garlic and cook 2 minutes until fragrant. Stir in the squash and 120 ml water, then blend until smooth. Stir in the Parmesan and season with salt. Cook the pasta in salted boiling water until al dente. Transfer it to the sauce with a ladle or two of pasta water and stir to coat. Serve topped with more Parmesan and plenty of black pepper.