Brine the Meat: Whisk together warm water, salt, brown sugar, and 1 tablespoon of lemon juice in a large bowl until dissolved. Add turkey and chicken pieces to the brine. Cover it and refrigerate it for one hour in a half. Drain meat in a colander, rinse with fresh water, and set aside.
Prepare Sofrito: In a food processor, blend onion, garlic, and jalapeño until finely chopped (about 10 seconds).Heat olive oil in a medium skillet over medium heat. Add the onion mixture with a pinch of salt and cook for 5–7 minutes, stirring often, until softened. Stir in parsley, oregano, and rosemary, and cook for an additional 1 minute. Remove from heat, transfer to a bowl, and chill uncovered for 20 minutes.
Make Lemon Aioli: Whisk together mayonnaise, 1 teaspoon salt, lemon zest, and 2 tablespoons lemon juice in a small bowl. Cover and refrigerate until needed.
Prepare Patties: Preheat the grill to high (450°F to 500°F). Process the brined meat in batches in a food processor, pulsing until it forms a coarse paste (about 7 pulses per batch).Combine the meat mixture with the chilled sofrito, mixing thoroughly by hand. Shape into six 7-ounce patties, tightly packed.
Grill Patties: Place patties on the preheated grill and cook uncovered, flipping often, until a thermometer reads 155°F (about 10–13 minutes). Top each patty with 1/4 cup of cheese, cover the grill, and cook for 2 more minutes until the cheese melts.
Assemble Burgers: Season tomato slices with salt and pepper. Spread 1 teaspoon of aioli and 1 teaspoon of barbecue sauce on each bun half. Place a grilled patty on the bottom bun, top with lettuce, and a slice of tomato, and cover with the top bun.
Enjoy your juicy turkey and chicken burgers! 🍔🍋