In a skillet, toast pecans until fragrant and starting to have slight brown spots. Pulse in a food processor until finely chopped. Set pecans aside for later.
Pulse mushrooms in the food processor until coarsely diced. Do this in batches if necessary to prevent getting the pieces too small. They should be about the size of a pea.
Combine diced mushrooms with onion and a splash of olive oil in a skillet. Saute until the mushrooms liquid has evaporated.
Stir in 1 TBS each tamari and balsamic. Saute until the liquid is absorbed.
In a large bowl, combine sauted mushroom mixture, pulsed pecans, garlic, freshly cooked short grain brown rice, flax seed meal, nutritional yeast, cumin, salt and red pepper. Stir until well combined.
Use your hands to form 4 patties from the burger mixture. Place in a skillet and cook over medium heat until golden on each side, about 8 minutes.
Teriyaki Sauce
In a small skillet, combine all ingredients for the teriyaki sauce. Whisk over medium heat until the mixture starts to boil. Let this simmer, whisking constantly for about 1 minute to allow the cornstarch to cook. Remove from heat.
Serving
Serve each burger patty on a bun with romaine lettuce, a slice of pineapple, a quarter of the teriyaki sauce, and jalapenos, if desired.