Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with aluminum foil.
Rub olive oil on cut-side of butternut squash halves; sprinkle each with salt and pepper. Lay squash, cut-side down, on prepared baking sheet.
Bake squash in the preheated oven until tender, about 1 hour. Scoop squash flesh into a bowl and mash.
Melt butter in a pot over medium heat. Cook and stir onion and garlic in melted butter until onion is slightly softened, 3 to 5 minutes. Add carrots; cook and stir until carrot and onion are tender, 5 to 10 minutes.
Stir mashed squash, marjoram, celery seed, cayenne pepper, salt, and black pepper into onion mixture; cook and stir until heated through, 5 to 10 minutes. Stir in chicken stock; bring mixture to a boil.
Gradually add cream and cream cheese to squash mixture; stir until cream cheese is melted and incorporated. Bring to a simmer and cook until flavors blend, 30 minutes.
