Preheat oven to 400 degrees F (200 degrees C).

Place squash on a rimmed baking sheet. Drizzle olive oil over squash and season with salt and pepper. Place garlic in a piece of aluminum foil, drizzle olive oil over garlic, and loosely wrap foil around garlic. Place garlic packet on the baking sheet with squash.

Bake in the preheated oven until squash is soft and golden brown, about 50 minutes. Cool squash slightly.

Melt 1/4 cup butter in a skillet over medium heat; cook and stir scallions until softened, about 4 minutes.

Scoop meat from cooked squash and transfer to a food processor. Squeeze garlic cloves from skins and add to squash in food processor; add scallions and chipotle peppers. Pulse until mixture is smooth. Add remaining butter, sour cream, Parmesan cheese, cream cheese, and lemon juice; pulse just until combined but not smooth. Season dip with salt and pepper.

Refrigerate dip for 1 hour.