Our 3 Best Tips for Legitimately Perfect Grilled Whole Cauliflower

Name: Our 3 Best Tips for Legitimately Perfect Grilled Whole Cauliflower
Ingredients: 2 large heads cauliflower (about 2 pounds each; 900g each); 3 quarts (2.84L) water; 3/4 cup plus 2 tablespoons(126g) kosher salt; 1/2 cup (120ml) Koikuchi shoyu, tamari, or saishikomi shoyu (see notes); 1/2 cup (120ml) sake; 1/4 cup (60ml) mirin; 5 tablespoons (60g) granulated sugar; 1 ½ teaspoons (8g) powdered dashi; 3 tablespoons rendered chicken fat or unsalted butter; 1 tablespoon (14g) toasted sesame oil; Shichimi togarashi, for serving; Lemon wedges, for serving