For the burgers: Coat a large saute pan with olive oil. Add the onions, season with salt and bring to a medium-high heat. Cook the onions, stirring occasionally, until they are soft and very aromatic, 7 to 8 minutes. Add the scallions, garlic and ginger and cook until fragrant, 1 to 2 minutes. Turn off the heat and let cool.
In a large bowl, combine the turkey, water chestnuts, cilantro, soy sauce, 1 tablespoon of the sambal oelek and the onion mixture. (Reserve the onion pan to cook the burgers in later.) Using your hands, squish everything together until really well combined.
Make and cook a little tester patty to be sure that the turkey is really well seasoned. Re-season if needed. If the burger is missing salt add more soy or just give a little sprinkey dink of salt.
When the burger mix is seasoned appropriately, shape it into 4 equal patties.
Coat the saute pan with olive oil and heat over medium-high heat. Place the burgers in the pan. Be sure not to crowd the pan, if you need to work in batches go ahead! Cook the burgers for 5 to 6 minutes on each side.
Preheat the oven to high broil.
Transfer the burgers to a baking sheet lined with a wire rack. Place the buns, cut side up, on the same rack. Transfer to a low rack in the oven and broil until the burgers are cooked through and the buns are toasted, 2 to 3 minutes. Remove the buns from the rack and top the burgers with cheese. Return to the oven and broil until the cheese melts, about 1 minute.
Stir to combine the mayonnaise and remaining 1 tablespoon sambal oelek in a small bowl. Schmear each side of the bun lightly with the sambaal mayo. Put a burger on each of the bottom buns and top each burger with a slice of tomato and onion and a piece of lettuce. Close up each burger, give each one a little squish and eat em' up!