Once the milk is incorporated, and no more lumps are in the mix, remove from heat and add 1 cup of each cheese, 1/2 a cup at a time, until all melted and mixed.
Slowly pour in milk, 1/2 a cup at a time, whisking after each addition. Continue cooking, stirring constantly for another 3 or so minutes, to lightly brown the flour mixture. Add in flour and seasoning, and quickly mix together with a whisk.
