If you intend to roast your own butternut squash: preheat oven to 425 degrees and toss 2 cups of peeled and cubed butternut squash with 1 tbsp olive oil, salt, and pepper. Spread onto a baking sheet lined with parchment paper and bake for 25 minutes, stirring once. Transfer cooked squash to a food processor or strong blender and puree until smooth, adding water as needed to thin.
Start with the breadcrumbs. Heat 1 tbsp butter over medium heat in a skillet. Add 1 clove of minced garlic and the breadcrumbs and toast, stirring frequently, for about 5 minutes until golden all over. Give one last toss with salt and pepper. Remove from skillet and set aside in a bowl.
Bring a large pot of salted water to a boil. Cook pasta according to package directions. Before straining, reserve 1 cup of the pasta water. Drain the rest of the water and set pasta aside.
Pour olive oil into the same skillet and saute carrot, shallot, the other 2 cloves of garlic, and dried oregano until soft and fragrant, about 3-5 minutes. Add tomato paste, red pepper flakes, and butternut squash puree and stir to combine, then pour in vodka and cook 2-3 minutes until most of the alcohol simmers out. Then, measure in coconut milk and butter and simmer 10-15 minutes. Finish with parmesan and stir until melted.
Toss pasta into the vodka sauce, adding reserved cooking water to thin as desired. Spoon into bowls and top with breadcrumbs, more parmesan, and chopped fresh basil.