Instructions

for the burger blend

Arrange turkey in single layer on rimmed baking sheet and freeze until very firm and starting to harden around edges but still pliable, 35 to 45 minutes.
Sprinkle gelatin over broth in small bowl and let sit until gelatin softens, about 5 minutes. Pulse mushrooms in food processor until coarsely chopped, about 7 pulses, stopping and redistributing mushrooms as needed; transfer to bowl.
Working in 3 batches, pulse turkey in now-empty processor until ground into 1/8‑inch pieces, about 20 pulses, stopping to redistribute meat as needed; transfer to separate large bowl.
Return 1/2 cup (about 3 ounces) ground turkey to again-empty processor along with softened gelatin, soy sauce, and baking soda. Process until smooth, about 2 minutes, scraping down sides of bowl as needed. With processor running, slowly add 2 tablespoons oil until incorporated, about 10 seconds. Return mushrooms to processor with paste and pulse to combine, 3 to 5 pulses. Transfer mushroom mixture to bowl with turkey and knead with your hands until combined.

to shape patties

With lightly greased hands, divide turkey mixture into 4 lightly packed balls, then gently flatten into 3/4‑inch-thick patties. Using your fingertips, press ­center of each patty down until about 1/2 inch thick, creating slight divot. Cover and refrigerate until ready to cook. (Patties can be refrigerated for up to 1 hour or frozen for up to 2 weeks. To freeze, stack patties, separated by parchment paper, wrap in plastic wrap, and place in ­zipper-lock freezer bag.)
FOR A SKILLET: Adjust oven rack to middle position and heat oven to 300 degrees. Season ­patties with salt and pepper. (If previously frozen, thaw at room temperature for 30 minutes before seasoning and increase baking time to 12 to 14 minutes.) Heat remaining 2 teaspoons oil in 12‑inch nonstick skillet over high heat until just smoking. Using spatula, transfer patties to skillet, divot side up, and cook until well browned on first side, 2 to 4 minutes. Flip patties and cook until well browned on second side, 2 to 4 minutes. Transfer patties to rimmed baking sheet, divot side down, top with cheese, if using, and bake until burgers register 160 degrees, 6 to 10 minutes. Transfer burgers to platter and let rest for 5 minutes. Serve ­burgers on buns.FOR A CHARCOAL GRILL: Freeze patties for 30 minutes. (If previously frozen, do not thaw.) Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes. Clean and oil cooking grate. Brush 1 side of patties with 1 teaspoon oil and season with salt and pepper. Using spatula, gently flip patties, brush with remaining 1 teaspoon oil, and season second side. Place burgers, divot side up, over hotter part of grill and cook until well browned on first side and meat easily releases from grill, 5 to 7 minutes. Flip, top with cheese, if using, and cook until well browned on second side and meat registers 160 degrees, 5 to 7 minutes. Transfer burgers to platter and let rest for 5 minutes. Serve on buns.