Cook garlic in a small cast-iron skillet over medium heat, stirring occasionally, until the skins have darkened and the cloves are soft inside, 12 to 15 minutes. Transfer to a cutting board. When cool enough to handle, remove skins and mash the garlic until smooth.
Meanwhile, melt butter in a medium saucepan over medium heat. Whisk in flour until combined. Gradually whisk in milk until smooth. Cook, whisking constantly, until thickened, 6 to 8 minutes.
Reduce heat to low and whisk in the mashed garlic, Parmesan, salt and pepper. Cook, whisking constantly, until the cheese has melted and the mixture is smooth, about 1 minute. Serve immediately.