Melt your butter in a small saucepan on a medium heat. When the butter has melted add in the flour and mix until it is well combined and bubbling.
Add half of your milk and mix it through until the mixture is smooth. Next add in the remaining milk and evaporated milk, mix well to combine.
Continue to heat, stirring constantly, until the mixture thickens. This should take about 8 minutes.
Mix in your grated cheese. Heat and stir for another minute or two or until the cheese has completely melted.
Season with salt and pepper. Serve your cheese sauce warm with your favorite sides.