In a small bowl, mix the mayonnaise and Sriracha. Refrigerate until you're ready to serve.
Heat one side of your Blackstone griddle to medium-low. Add the oil and onion and season with salt. Cover the griddle and cook, stirring occasionally, until onions are softened, 10 to 15 minutes.
While the onions are cooking, combine the turkey, Worcestershire sauce, ¼ teaspoon salt, and ¼ teaspoon pepper in a bowl. Mix well and divide the mixture into 4 pieces. Shape each piece into a ball, taking care not to pack the meat too tightly.
Heat the other side of the griddle to medium-high. Place each burger ball on the griddle and use a burger press or large spatula to firmly press down on each burger until they're "smashed" to about ⅜-inch thick.
Cook, flipping once, until cooked through, 4 to 5 minutes per side.
Top each patty with cheese.
While the cheese is melting, push the onions off to one side (they should be soft and golden at this point), and place the buns, cut side down on the griddle. Let them toast for 1 to 2 minutes.
To assemble, spread about 1 ½ teaspoons of Sriracha mayo on the top half of each bun. Place a burger patty on the bottom half of each bun, top with onions, and the top bun. Devour.