To prepare the kombu dashi, place kombu, mushrooms, and 2½ cups* of water in a small saucepan. Set to medium and turn off the heat right before it comes to a boil.
Strain to a large bowl or cup and reserve the mushrooms and kombu for other dishes. It should yield about 2¼ cups.
Next, heat a large non-stick skillet with a tablespoon of oil. Sauté mushrooms until a thin brown crust forms and is aromatic. Push the mushrooms to the side of the pan and sauté onion until tender, adding more oil if needed.
Stir in a tablespoon of curry powder and mix to combine.
Pour in the kombu dashi, mirin, soy sauce, mushrooms seasoning, sugar (if used), and add in the udon. Cover the pan with a lid and cook until flavors meld and the udon is fully cooked through.
Meanwhile, mix a teaspoon of cornstarch with 1 tablespoon of water until incorporated.
When the sauce has reduced to almost half, stir in the slurry for a thicker sauce. Note: See below for curry cubes option.
Taste test and adjust seasoning accordingly. Garnish with chopped scallions before serving.