Pulse garlic, goat cheese, yogurt, 1 cup mint, 1 cup parsley, 2 Tbsp. oil, and 1 Tbsp. 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 core. Cut each half into 3 wedges, keeping core intact. Drizzle wedges with oil to coat and season all over with salt. Grill until deeply charred on all sides (pretty much blackened) and a paring knife easily slips through the center, about 8–10 minutes per side. Transfer to a cutting board and let cool 5 minutes. Cut each wedge in half crosswise.

Toss cucumbers, remaining 1 cup mint, remaining 1 cup parsley, and remaining 1 Tbsp. 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; drizzle with more oil.

Do Ahead: Raita can be made 1 day ahead. Cover and chill.