Preheat the oven to 400 degrees Fahrenheit.
Line a baking tray with foil.
Add the cubed butternut squash onto the sheet pan.
Toss the butternut squash cubes in the olive oil and bake them on the parchment paper or foil-lined sheet pan for 25 minutes.
While the butternut squash bakes, add some water to a large pan and place it on a stovetop set to medium heat. Bring it to a boil. While it is at an active simmer, add your pasta to the water and cook it according to package instructions. When the pasta is al dente, drain it (reserve a cup of the pasta water) and set the pasta aside in a serving bowl with a drizzle of olive oil and covered with a tight-fitting lid.
And, also while the butternut squash is baking, peel the fresh ginger and grate it using a microplane grater. If a microplane grater isn't available, then finely dice the peeled ginger and set it aside.
Remove the roasted butternut squash from the oven and add it to a food processor or blender. Then, add in the coconut milk, smoked paprika, coriander, and grated ginger. Blend on high till mixture is creamy.
Add this spicy butternut squash sauce to the cooked pasta and stir it well.
If the sauce is too thick, use about a quarter cup of the reserved pasta water to thin out the sauce. You could use some vegetable broth instead of the pasta water.
Season this spicy butternut squash pasta with salt (or kosher salt) and black pepper to taste.
Completely optional is to serve it with a sprinkling of chopped curly or flat leaf parsley.