In a large bowl, combine the ground turkey, grated onion, minced garlic, beaten egg, Worcestershire sauce, Dijon mustard, smoked paprika, salt, black pepper, garlic powder, and olive oil.

Using your hands, mix gently until just combined — do not overwork the mixture. Overworking makes tough, dry patties.

Divide the mixture into 4 equal portions (about 6 oz each) and form into patties roughly 3/4-inch thick and slightly wider than your bun, as they will shrink slightly during cooking.

Press a shallow thumbprint dimple into the center of each patty. This prevents puffing and helps the burger cook evenly.

Place patties on a parchment-lined plate, cover loosely with plastic wrap, and refrigerate for at least 20 minutes (up to 24 hours). This step is crucial for patties that hold together on the grill.

Preheat your gas or charcoal grill to medium-high heat, around 400–425°F. Clean the grates thoroughly.

Using tongs, rub the grill grates with a folded paper towel soaked in vegetable oil. This prevents sticking and helps develop a proper sear.

Make the smoky aioli: whisk together mayonnaise, sriracha, and lemon juice in a small bowl. Season to taste and refrigerate until ready to serve.

Remove the chilled patties from the refrigerator. Place them directly on the oiled grill grates.

Grill for 6–7 minutes on the first side without moving them. You want a firm, charred crust to form before flipping — this is what gives you clean release from the grates.

Flip the patties carefully using a wide spatula. Grill for another 5–6 minutes on the second side.

In the last 60–90 seconds of cooking, place a slice of cheese on each patty and close the grill lid to melt.

Use an instant-read thermometer to verify the internal temperature has reached 165°F at the thickest point. This is the safe temperature for ground poultry — do not skip this step.

Transfer the burgers to a clean plate, tent loosely with foil, and rest for 2 minutes before serving.

Butter the cut sides of the brioche buns and place face-down on the grill for 30–45 seconds until golden and lightly toasted.

Spread smoky aioli generously on both the top and bottom bun.

Layer in this order for the best structural integrity: bottom bun, aioli, lettuce (acts as a moisture barrier), patty with cheese, tomato, red onion, top bun with aioli. Serve immediately.