Preheat oven to 400°F.
On a baking sheet lined with parchment paper, toss together the butternut squash, olive oil, garlic powder, smoked paprika, chili powder, and season with salt and pepper. Bake for 25-30 minutes, until the squash is tender.
Meanwhile, prepare the breadcrumbs: heat the olive oil in a large skillet over medium heat. Add breadcrumbs and toast, stirring frequently, until golden – 2 to 3 minutes. Season with salt and pepper. Transfer to a bowl, and add parmesan and parsley. Toss to combine.
Cook the pasta according to package instructions. Drain, reserving about 1/2 cup of the cooking water.
Once the squash is tender, remove and transfer to a blender with the cream. Blend until smooth.
Wipe out the skillet you used for the breadcrumbs with a paper towel. Drizzle with olive oil and add the chopped sun-dried tomatoes. Sauté for 2 minutes.
Stir in the butternut puree and gradually add about 1/4 cup pasta cooking water, stirring until combined - add more as needed. Taste and adjust seasonings.
Add the pasta to the sauce, tossing to combine. If too thick, add more of the reserved cooking water. Divide the pasta between plates. Top with breadcrumbs, burrata, and pomegranate seeds. Serve.