In a small saucepan, heat soy sauce, rice vinegar, brown sugar, ginger, and garlic to a boil. Reduce to a simmer until thickened, about 5-6 minutes. Set aside to cool.
Add salmon to a food processor. Pulse until ground. Remove blade and add in ¼ cup of teriyaki sauce, green onions, panko, and 2 tablespoons pineapple juice from can. Mix just until combined. Form into 4 patties, if you have time, chill for 10 minutes. (This step isn't necessary, it just helps the patties to stay compact.)
Heat a large non-stick skillet to a medium-high heat. Add coconut oil. Once the oil has melted, add patties, cook until golden brown on both sides and cooked through, about 2 minutes per side. Glaze with more teriyaki sauce at the last minute.
Brush pineapple with sauce, remove patties from pan and add pineapple. Cook until caramelized on both sides, about 30 seconds per side.
In a small bowl combine cabbage and sesame oil. Season to taste with salt and pepper.
Place cabbage on bottom of bun, top with patty, and pineapple.