Preheat the oven to 350 degrees F.
Put the mushrooms on a rimmed baking sheet and bake for 5 minutes. Let cool. Do not turn off the oven.
Assemble the skewers so that each holds 2 pieces of tempeh, 2 pieces of tofu, 1 mushroom, and 1 piece each of zucchini, red bell pepper, yellow bell pepper, and onion. Alternate the items to create an appealing look.
Line a baking sheet with parchment paper and arrange the skewers on it. Bake for 12 minutes. Make sure the tofu triangles don’t touch the edge of the baking sheet or each other, or they will stick. Brush the skewers with the glaze and bake for 3 minutes longer. Serve hot over the brown rice.