Preheat an oven to 350 degrees. Meanwhile, melt the butter and pour it into a large mixing bowl. Then, whisk the garlic, gochujang, honey, vinegar, and soy sauce into the butter.
Quarter both the zucchini and mushrooms into chunky pieces. Toss them into the mixing bowl with the first amounts of salt and pepper. Toss the ingredients until all the veggies are coated in sauce.
Use a slotted spoon to transfer the vegetables to a 9-inch cast iron skillet or oven-safe pan. There will be some sauce remaining in the bowl which you should reserve.
Lay individual 3-oz salmon filets over the vegetables in the skillet. Sprinkle the remaining salt and pepper over the salmon. Then, use a marinade brush to collect the remaining sauce in your mixing bowl and spread this over the salmon.
Bake the skillet in your oven for 20 minutes. Then, turn on your oven broiler to high heat. Bake the skillet for an additional 10-15 minutes or until your salmon has crispy edges and a light golden brown coloring.