Brown Butter Sweet Potato Alfredo

unsalted butter, (browned)

medium sweet potato (cubed into 2-inch cubes)

all-purpose flour

whole milk

water, (divided)

freshly grated Parmesan cheese

dried spaghetti pasta, (cooked according to the directions on the box)

cayenne pepper, (more or less depending on heat preference)

Salt and pepper (to taste)