Preheat oven to 425F and line two large sheet pans with foil.
Place the carrots on one pan and the cabbage on another. In a small bowl, mix the gochujang, cumin, salt, garlic, ginger and 3 Tbls of oil. Pour half the sauce over each pan of vegetables and mix with your hands so that the marinade gets everywhere.
Make sure that the carrots and cabbage are in a single layer, then place the pans in the oven for 35 to 40 minutes until the vegetables are tender and blackened at the edges.
Meanwhile, put 2 Tbls of oil and the white wine vinegar into a large bowl. When the carrots and cabbage are roasted, transfer them to the bowl while still hot and toss them in the oil and vinegar. Pile the vegetables onto a large plate and serve.