Serves 6 to 8
Preheat oven to 350 degrees.
Rub sweet potatoes with oil, season with salt and pepper, and set on a baking sheet. Roast in oven for 1 to 1 1/2 hours or until soft. Remove from oven and set aside.
Increase oven temperature to 425 degrees.
Melt half the butter in a small skillet set over medium-high heat. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook for one minute until butter is foamy and lightly browned. Remove from heat and stir in brown sugar.
Peel potatoes and measure out 1 cup roasted potato. Transfer to a food processor or blender and process on high. Drizzle in butter mixture and process until smooth, about 1 minute.
Melt remaining butter in a small pot set over medium heat. Whisk in flour and cook for 2 to 3 minutes, until light brown in color. Add 1/4 teaspoon salt and 1/4 teaspoon pepper, then whisk in milk, stirring as necessary and cooking until thickened, about 3 minutes. Remove from heat and transfer to a large bowl. Whisk in yolks, one at a time, until incorporated. Whisk in sweet potato mixture. (This base can be set aside at room temperature until ready to bake the souffle; you may cover and refrigerate it if done in advance, but it must be brought to room temperature before proceeding.)
Wrap aluminum foil around a 7-cup souffle dish to about 3 inches above the rim. Grease the inside of the dish and aluminum foil with nonstick cooking spray. Set it onto a rimmed baking sheet for easier handling.
Whip egg whites on low with a handheld electric mixer until foamy. Add a pinch of salt and cream of tartar. Whip on high until stiff peaks form.
Gently fold about 1/3 of the beaten whites into sweet potato mixture until uniform. Repeat with remaining egg whites. Transfer mixture to prepared souffle dish and place in oven. Reduce heat to 375 degrees and bake until souffle has risen 2 to 3 inches above the top of the dish and is nicely browned, about 1 hour. Remove from oven and allow souffle to sit no longer than 5 minutes before serving .
To serve, plunge two large serving spoons back to back in the middle of the souffle -- this will help prevent the souffle from falling. Serve immediately.