To make your teriyaki sauce, add all ingredients to a small sauce pot. Whisk well. Then place over medium heat and continue whisking briskly until the sauce begins to thicken - tis should take 4-5 minutes. Turn heat to low and continue whisking for another minute and then turn off heat and set aside. Tip: add more sugar if you like a sweeter sauce.
Prep your pineapple, onion, lettuce and portobellos. Mash your avocado.
Turn oven to 450 degrees.
Layer two baking sheets with parchment paper. On one, add the sliced pineapple. On the other, the mushrooms. Lightly brush the pineapple with teriyaki sauce. Heavily brush the portobellos with sauce. Tip: Use a rimmed baking sheet or a glass baking dish for the mushrooms, since they get juicy. I added about 1 teaspoon sauce to each side of the mushrooms.
Bake pineapple for about 10 minutes, just until they soften and caramelize a bit. Bake the mushrooms 18-20 minutes, or until they are super tender. If needed, flip mushrooms half way through and re-brush with sauce.
About 5 minutes before mushrooms are done, place your buns in the oven to warm them.
Assemble burgers: Add a layer of mashed avocado. Then a portobello cap. Then one or two pineapple rings. Then onions and lettuce and finally, a teriyaki sauce slathered top bun. Serve warm!