Preheat oven to 400 F. If needed, cut cod fillets so they fit easily in the skillet, reserving marinating liquid. Heat canola or vegetable oil in a large skillet over medium-high heat. When hot, add carrots and cook until beginning to soften.
Add mushrooms and butter, then cook, stirring occasionally.
Trim the ends off scallions, then cut into pieces. Add to the skillet and sauté until blistered. Season with kosher salt, stir, then transfer to a bowl.
Carefully add cod fillets to the warm, preheated pan. Cook, then gently use a fish spatula to flip the fish over, being careful not to break it. Return cooked vegetables to the pan, then pour reserved miso marinade on top. Transfer the skillet to preheated oven and cook.
Thinly slice remaining scallion (discard the root), then sprinkle on miso cod along with a generous sprinkle of sesame seeds for garnish. Serve immediately.