Use damp paper towel to gently clean the kombu piece, then soak it in 3 tablespoons of water. If you don't have or can't find kombu, you can use vegetable stock.
Remove the tofu block from its packaging. Line a plate with paper towel, place tofu on top. Set a heavy plate with something heavy on it over the tofu. Press the tofu like that for 10 minutes.
While the tofu is pressed, prep the vegetables: shred cabbage, julienne carrot and slice onion.
After 10 minutes, pat the tofu dry and slice into 1/2'' thick pieces. Fry them in a pan over medium-high heat until crispy. Transfer to a plate lined with kitchen towel to absorb excess oil. Cut into thin strips.
Prepare udon noodles according to instructions on the package. If you use the frozen udon I recommend, you just need to boil it for 2-3 minutes.
Place a pan over medium-high heat, add some oil and add onion. Stir and cook for 2 minutes until onion is fragrant.
Add cabbage and carrot. Stir frequently, add a pinch of salt and pepper and cook for about 2 minutes.
Add udon noodles, tofu strips, soy sauce, mirin, sesame oil and the liquid from soaking kombu (discard the kombu, we only use the liquid). Mix well and adjust seasoning.
Transfer to serving plates and top with scallions and seaweed strips.