Kitsune Udon

Break kombu into 2-inch pieces; this should equal about 2 cups, loosely packed. Bring water and kombu to a gentle boil in a medium saucepan over medium heat; boil for 5 minutes. Remove from heat, then remove and discard kombu. Sprinkle in bonito flakes and bring to a simmer over medium heat, about 2 minutes. Once simmering, remove from heat, strain, and discard solids. Place dashi back into the saucepan and set aside.

Place aburaage in a medium bowl. Cover with hot water and let soak until light and fluffy, about 5 minutes. Strain, allow to cool briefly until cool enough to handle, and gently press aburaage with your hands to squeeze out any excess water.

Bring 1 cup dashi, 1 1/2 tablespoon soy sauce, 1 tablespoon mirin, and sugar to a boil in another medium saucepan over medium-high heat. Reduce to a simmer over medium-low heat and add the soaked aburaage. Cook, covered, until the majority of the liquid is absorbed, about 5 minutes. Flip aburaage halfway through.

Bring the remaining 4 cups of dashi to a gentle boil over medium heat. Stir in salt, remaining 1 tablespoon soy sauce, and remaining 1 tablespoon mirin. Add frozen udon noodles; cook over medium heat, stirring occasionally, until noodles have separated and are tender yet firm to the bite, about 2 minutes.

Divide noodles and broth evenly into 2 bowls. Top with seasoned aburaage and sliced scallions.