Blanch the aburaage in boiling water for 1-2 minutes to remove excess oil. Gently press out water and slice in half or into smaller pieces.
In a small pot, combine dashi stock, soy sauce, mirin, and sugar for aburaage. Add the prepared aburaage and simmer over medium-low heat until the liquid is mostly absorbed and the tofu is sweet and juicy.
In a separate pot, combine dashi stock, soy sauce, mirin, sugar, and salt for the broth. Bring to a gentle simmer over medium heat. Taste and adjust seasoning if needed.
In a large pot of boiling water, cook the udon noodles according to package instructions. For fresh udon, this usually takes 2-3 minutes. Drain well.
Divide the cooked udon noodles into serving bowls. Pour the hot dashi broth over the noodles.
Top each bowl with the sweet aburaage. Garnish with thinly sliced green onions and a sprinkle of shichimi togarashi, if desired. Serve immediately.
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