In a heavy bottom sauce pan, melt butter over med-low heat, add in sage leaves; cook, stirring constantly, until butter is golden brown. Remove from heat. Remove sage leaves only and add them to the topping mixture.
Return brown butter to heat and add flour. With a wire whisk stir mixture constantly until bubbly, about 2-3 minutes. Slowly pour in milk, stirring continuously until butter flour and milk are well combined. Allow sauce to come to a gentle boil, stirring occasionally.
Reduce heat to low and gradually add shredded cheese, stirring after each addition until cheese is melted and incorporated into sauce. Remove from heat.
Stir in cayenne and black pepper. Adjust according to taste. The sauce should not need salt, but add if necessary.