Preheat oven to 450°. Toss broccoli with grated garlic, sambal oelek, 1 Tbsp. vinegar, and ¼ cup oil on a rimmed baking sheet; season with salt and pepper. Roast, tossing occasionally, until tender and browned in spots, 20–25 minutes.
Step 2
Meanwhile, whisk scallions, ginger, sliced garlic, 1 tsp. salt, ¼ tsp. pepper, and remaining ½ cup vinegar and ½ cup oil in a large bowl. Add kale; toss to coat. Let sit at room temperature at least 15 minutes and up to 1 hour.
Step 3
Cook noodles according to package directions. Drain; rinse under cold water. Add noodles and warm broccoli to kale and toss to coat. Divide among bowls and top with mint, sesame seeds, and more scallions.