Preheat oven to 375°F. Butter six 10-oz ramekins and dust with grated parmesan, tapping out excess. Place on a baking sheet and chill until ready.
Melt butter in a medium saucepan over medium heat. Add flour and whisk until bubbly, about 1 minute. Add milk a little bit at a time, whisking smooth after each addition, until all of the milk has been added. Bring to a boil, reduce to a gentle simmer, and cook until thickened, about 5 minutes. Whisk in salt, pepper and dry mustard.
Transfer to a bowl and let cool slightly. Whisk in egg yolks, cheddar and herbs.
Use a stand mixer fitted with a whisk attachment to beat egg whites and cream of tartar on medium speed until loose and foamy, about 3 minutes. Increase speed to medium-high and beat until peaks are stiff.
Stir ⅓ of the egg whites into the egg yolk base to lighten. Gently fold in the rest of the egg whites, stopping when a few streaks are still visible. Fold in cubed Savory Butter Rolls.
Divide the soufflé mixture between the ramekins. Bake until risen and golden brown, 25-30 minutes. Serve immediately.
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