In a small saucepan, melt the butter over low-medium heat. Once fully melted, sprinkle the flour on top of the melted butter and mix with a spatula until fully incorporated and a paste has formed. Continue mixing for 1-2 minutes.
Slowly pour in the milk while continuously whisking. When the mixture has thickened enough to coat the back of a spoon, add in the cheese and whisk until the cheese has all melted and mixture is uniform.
Add the grille sauce and whisk until combined.
Add salt and pepper to taste and serve hot.
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