In a large pot, melt 1/4 cup butter over medium heat. Whisk in the flour to create a roux, cooking for about 1 minute until bubbly.
Gradually whisk in the milk, ensuring there are no lumps. Cook until the sauce thickens, about 5 minutes, stirring constantly.
Reduce the heat to low and stir in the shredded cheddar cheese, Monterey Jack cheese, and cream cheese until smooth and creamy. Season with salt and pepper.