Step 1

Mash half of 1 avocado with a fork in a medium bowl until smooth (reserve remaining half for topping burger). Add Worcestershire, garlic powder, cumin, 3 Tbsp. mayonnaise, 2 tsp. Sriracha, and 1½ tsp. salt. Grate half of the onion (as in, half of the half, or one-quarter of the whole) on the medium holes of a box grater into bowl. Mix with a fork to combine. Add turkey and mix thoroughly with clean hands until mixture is homogeneous (it will feel very wet and soft, which is okay).

Step 2

Drizzle 1 Tbsp. oil on a large plate. Using oiled hands, form turkey mixture into 4 balls, place on plate, and press down into patties 4–4½" across (they’ll shrink as they cook). Chill, uncovered, at least 10 minutes and up to 2 hours (this step will help keep them firm). If chilling for more than 2 hours, cover with plastic and chill up to 2 days.

Step 3

Meanwhile, stir remaining ½ cup mayonnaise and 2 tsp. Sriracha in a small bowl and season with a pinch of salt.

Step 4

Thinly slice remaining onion and toss with cabbage in a medium bowl.

Step 5

Heat 2 Tbsp. oil in a large nonstick skillet over medium. One by one, carefully slide patties off plate into skillet. Cook, shaking skillet a couple of times to make sure patties aren’t sticking, but not pressing down on them, until dark brown underneath, about 5 minutes. Turn and cook on second side until burgers are fully cooked, about 5 minutes more. Transfer to a wire rack and let rest while you finish assembling.

Step 6

Thinly slice remaining 1½ avocados. Add lime juice and remaining 1 Tbsp. oil to cabbage mixture and toss to combine; season with salt.

Step 7

Divide Sriracha mayo among cut sides of buns, spreading to edges. Place patties on bottom buns, then shingle avocado slices over. Heap slaw over avocado, then close burgers with top buns.