Step 1

Combine woodear and morels mushrooms in a medium saucepan and cover with 1 1/2 quarts water. Bring to a boil over high heat, then remove from heat and let rest 10 minutes while mushrooms rehydrate. Remove mushrooms with a slotted spoon and set aside. Add fresh mushroom scraps and stems, botton 1-inch of scallions, garlic cloves, onion, and kombu to pot. Bring to a boil and reduce to a sub-simmer. Cook for 20 minutes.

Step 2

Meanwhile, rip out the tough central stems from the woodear mushrooms and discard. Slice woodears and morels into strips and transfer to a small bowl. Slice fresh mushrooms and add to bowl (if using enoki, reserve separately). Finely slice remaining scallion tops and set aside.

Step 3

When broth is simmered, strain through a fine mesh strainer and return to pot, discarding solids. Add soy sauce and mirin and season to taste with salt. You should have about 1 quart of broth. Keep warm.

Step 4

Heat 1 tablespoon vegetable oil in a wok or a 12-inch skillet over high heat until lightly smoking. Add mushrooms (except for enoki, if using) and stir-fry until lightly browned and completely tender, about 2 minutes. Season to taste with salt and transfer to a plate. Add remaining tablespoon oil and heat until lightly smoking. Add cabbage and stir-fry until tender and charred in spots, about 2 minutes. Season to taste with salt. Transfer to plate with mushrooms.

Step 5

Cook udon in boiling water according to package directions, adding fried tofu to the water as they cook to heat. Strain and divide noodles between two serving bowls. Pour hot broth over noodles. Top with chopped scallions, stir-fried mushrooms and cabbage, raw enoki (if using), and fried tofu. Serve immediately.