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Prepare 4 (8-ounce) ramekins by greasing them with softened butter and then coating them with sugar, tapping out any excess.
Make a thick bechamel sauce base by melting the 3 tablespoons of butter over low-medium heat in a thick-bottomed pot. Just as the foam subsides, add the flour, stirring constantly with a whisk to prevent lumps. Cook for 2 to 3 minutes to coat the flour with fat and remove the starchy taste; do not allow the roux to brown. Add the warm milk to the mixture and continue to whisk until smooth and thick. Remove from the heat. Beat in the sugar and then the egg yolks 1 at a time. Season with salt, pepper, and nutmeg. Stir in the cheese until incorporated evenly. Chill the mixture while whipping the egg whites.
In a separate clean bowl beat the egg whites and cream of tartar just until soft peaks form. Fold 1/3 of the beaten whites into the bechamel mixture to lighten it. Then gently fold in the rest. Pour the batter into the prepared ramekins and place on a cookie sheet. Bake on the middle rack for about 25 minutes.
The souffle is done when it has puffed over the rim, the outside is golden, and the center jiggles slightly.