Pulse garlic, goat cheese, yogurt, 1 cup of mint, 1 cup of parsley, 2 Tbsp. of oil, and 1 Tbsp. of lemon juice in a food processor until smooth and pale green. Transfer raita to a medium bowl; season with salt.

Prepare a grill for medium heat. Cut cabbage in half through the core. Cut each half into 3 wedges, keeping the core intact. Drizzle wedges with oil to coat and season all over with salt. Grill until deeply charred on all sides and a paring knife easily slips through the center, about 8-10 minutes per side. Transfer to a cutting board and let cool for 5 minutes.

Toss cucumbers, remaining 1 cup mint, remaining 1 cup parsley, and remaining 1 Tbsp. of lemon juice in a medium bowl. Season salad with a big pinch of salt and toss again.

Spread raita over plates; place a few pieces of cabbage on each. Top with salad and Corn Nuts. Sprinkle with Aleppo-style pepper and drizzle with more oil. Do Ahead: Raita can be made 1 day ahead. Cover and chill.