Cook pasta in a saucepan over stovetop, and cook chorizo with olive oil in a large skillet over medium-high heat.
While those are cooking, place cubed sweet potato in a microwave safe bowl and microwave for 10 minutes, or until sweet potato is soft. If you don't want to use the microwave, you can roast the sweet potato at 400° for 20 minutes or so.
Once the pasta is cooked, place it in a strainer and set it aside. Once the chorizo is cooked, scoop it out with a slotted spoon (I placed it in the strainer with the pasta), and then add butter to the skillet.
Add the shallot and garlic to the skillet and stir for about 30 seconds or until shallot is translucent.
Next, add cooked sweet potato and chicken broth to the skillet and bring to a simmer. Once simmering, stir in the milk and whipping cream.
Next, add about half the mixture to a blender and pulse until smooth; pour the blended soup back into the skillet and stir to combine. Last, stir in the pasta and chorizo, and add salt and pepper to taste.