In a small bowl combine dikon radish, tsp of Gochugar, and a splash of rice wine vinegar. Set aside.
Heat large skillet over medium heat
You want to work in small batches, cooking all things separately. You'll want a large serving platter or sheet pan ready to transfer cook vegetables to.
Once pan is hot, add tbs of oil and add in shiitake mushrooms. Lightly season with salt, pepper, and garlic powder. Cook for about 5-8 minutes or until they reach desired tenderness. Remove mushrooms from pan onto platter or sheet pan and lightly drizzle with sesame oil! Toss and cover lightly with foil to keep warm
In the same pan, add in another tbs of oil, and toss in carrots. Drizzle with a little soy sauce and cook 2-4 minutes. Transfer to sheet pan with mushrooms and recover
Next add 1 more tbs of oil to the pan and toss in eggplant. Drizzle with soy sauce and cook 2-4 minutes. Remove and place them with carrots and mushrooms.