5 Large Eggs (Separated, plus 1 additional egg white)
1/4 teaspoon Cream of Tarter
Make the sauce: In the strainer, rinse the roasted peppers well under cold water. Pat dry with paper towels. Transfer to the bowl of the blender and add the water, olive oil, and salt. Blend until smooth, 20 to 30 seconds. Set aside.
Make the béchamel: In the large bowl, whisk together the flour, cornmeal, and paprika. Melt the butter in the medium saucepan over medium heat. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute. Remove from the heat, add the flour mixture, and whisk well to remove any lumps. Return to the heat and cook for 1 to 2 minutes, whisking constantly. Remove from the heat again and add the milk slowly, whisking constantly to remove any lumps. Return to the heat and bring to a boil, whisking constantly. Boil for 1 to 2 minutes, then add the corn kernels and continue to cook for 3 to 4 minutes, whisking until the sauce has thickened and the corn is cooked through. Remove from the heat and whisk in the Parmesan, basil, and salt. Whisk in the egg yolks and transfer to the large bowl. Set aside.
Preheat the oven to 400°F and position an oven rack in the bottom third. Generously butter the soufflé dish (including the rim), coat it with finely grated Parmesan, and tap out the excess.
Whip the egg whites: In the very clean bowl of the stand mixer, whip the 6 egg whites and the cream of tartar on medium speed until they form firm peaks. You may also use a hand mixer and a medium bowl. Be careful not to overbeat. With the spatula, gently stir one-fourth of the egg whites into the béchamel to lighten the mixture. Fold in the remaining whites just until there are no more streaks of whites.
Fill the dish and bake: Transfer the batter to the prepared baking dish and place on the baking sheet. Bake for 20 minutes. Then reduce the oven temperature to 375°F and bake for 18 to 22 minutes longer, until set and firm to the touch. While the soufflé is baking, transfer the red pepper sauce to the small saucepan and heat through. Serve the soufflé immediately, accompanied by the sauce.