Place acorn squash cut-side down on a large microwave-safe plate. Cook in the microwave until very soft, about 15 minutes. Let cool until easily handled, about 5 minutes.
Peel squash, discarding skin. Combine squash flesh, olive oil, salt, pepper, garlic, and rosemary in a bowl; mash to combine.
Pour vegetable broth into a saucepan; bring to a simmer over medium heat.
Melt 2 tablespoons butter in a large pot over medium heat. Add onion; cook and stir until softened, about 5 minutes. Stir in rice until coated with butter. Pour in wine, stirring until reduced, about 3 minutes.
Ladle 1/3 of the vegetable broth into the pot; cook and stir until absorbed. Repeat this process twice more, stirring constantly, until rice is tender, 15 to 20 minutes. Season with salt, pepper, and Italian seasoning.
Stir fontina cheese and Parmesan cheese into the rice until melted. Add mashed squash and remaining 2 tablespoons butter; stir until butter is melted and squash is heated through, 2 to 4 minutes.