Cook pasta according to package directions, drain and place into a large bowl. Melt butter in a large saucepan over medium heat.
Add garlic and cook for a minute until fragrant. Add flour and cook for a minute to brown. Whisk in milk, monterey jack cheese, cheddar cheese, salt, pepper and paprika.
Continue to cook over medium heat, whisking constantly until the sauce has thickened and the cheese is fully melted. Mix sauce with cooked pasta.