Preheat the oven to 350 degrees F (175 degrees C).

Toss butternut squash, olive oil, salt, and black pepper together in a bowl. Place on a baking sheet.

Bake in the preheated oven until tender, about 1 hour.

Transfer baked squash to a 4-quart pot and add chicken stock until level with squash. Add ginger and nutmeg and bring to a simmer, about 15 minutes.

Fill blender halfway with soup. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour into a pot. Repeat with remaining soup. Add creamer and stir to combine.