Whisk together all of the ingredients except the sesame oil in a small saucepan over medium heat.
When the mixture comes to a simmer, reduce heat to medium-low and continue to simmer, stirring occasionally, for about 15 minutes, or until slightly thickened—it should be thinner than regular barbecue sauce, but thicker than teriyaki sauce.
Stir in the oil and set aside.
To make the bowls:
Heat 1 tablespoon of sesame oil in a large non-stick skillet or wok over medium-high heat.
Add the broccoli and stir fry for 1 minute.
Carefully add the water to the skillet and cover; let the broccoli steam for about 2 minutes, until bright green and tender.
Add the zucchini, pineapple, red pepper and soy sauce to the skillet. Cook, stirring constantly, 3–5 minutes more, or until all the vegetables are tender-crisp.
Divide the vegetables into 4 bowls and wipe the skillet clean with a paper towel.
Return the skillet to medium-high heat. Add the remaining sesame oil and swirl to coat, then add the tofu. Cook the tofu until lightly browned and crisp on all sides, turning occasionally, 8–10 minutes.
Pour ½ cup of the sauce over the tofu and toss to coat; cook 2 minutes more, until sauce has thickened and the tofu is coated.
Divide the tofu into the bowls, then add the quinoa and red cabbage. Drizzle with the remaining sauce and garnish with sliced green onions and sesame seeds.