In a large Dutch oven, bring squash and water to cover to a boil over medium-high heat. Reduce heat to medium-low; simmer until squash is fork tender, 8 to 10 minutes. Drain well, reserving 2 cups cooking liquid. Transfer squash to a medium bowl, whisk smooth, and set aside.
In the same Dutch oven, melt 2 tablespoons butter over medium heat. Add shallot and thyme; cook, stirring occasionally, until softened and fragrant, 2 to 3 minutes.
Stir in reserved cooking liquid, milk, salt, and pepper. Bring to a boil. Slowly stir in polenta. Reduce heat to medium-low; simmer, uncovered, stirring frequently, until thickened, 25 to 30 minutes.
Stir in remaining 2 tablespoons butter, squash purée, and Parmesan. Cook until warmed through, 1 to 2 minutes. Serve immediately. Garnish with Parmesan and thyme, if desired.
Notes
*We used Bob’s Red Mill Polenta.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/butternut-squash-polenta-recipe/