Roast or microwave the acorn squash until tender. Scoop out the meat into a bowl, set it aside. If it's your first time cooking acorn squash, check the note below.
Make the soup:
In a soup pot, melt the butter over medium-high heat, add the onion and celery, and sauté until the onions are translucent, for about 3 minutes.
Add the flour and spices to the veggies and stir to combine. Cook to toast the spices and the flour while stirring, for about 1 minute. Add the broth and milk and bring the mixture to a simmering boil.
Add the acorn squash meat to the soup, stir to combine, reduce the heat to medium-low, cover with a lid, and cook for 10 minutes.
Make it smooth:
If using an immersion blender, purée the soup in the pot until smooth.
If using a traditional blender, ladle the soup into the blender, filling it no more than halfway, place the lid, and open the venting top a little to let some of the steam escape. Blend slowly at first, gradually increasing speed, until smooth.Transfer the puréed soup into an empty soup pot or another bowl. Repeat with the remaining soup in the pot. Pour the blended soup back into the pot, stir to combine, and serve.