Slice the tofu into 3 slabs vertically, press again to dry the inside, then cut into small cubes and place on a greased baking sheet. Drizzle with 1.5 teaspoons olive oil and 2 teaspoons low sodium tamari or soy sauce.
Preheat the oven to 425 degrees. In a medium mixing bowl add the broccoli florets, sweet potato, and carrots plus the remaining 1 1/2 teaspoons olive oil, salt and black pepper. Toss them until they're coated then place onto the other part of the baking sheet and spread out into an even layer. Add the pineapple to a corner of the sheet and bake for approximately 30 minutes, tossing all ingredients at 15 minutes, until the tofu is golden and crisp on the edges.
While the tofu and broccoli bake, make the teriyaki sauce. In a saucepan over medium-high heat, whisk together all of the ingredients for the sauce except the teaspoon of arrowroot mixed with a teaspoon of water. Bring the sauce to a boil then whisk in the arrowroot-water slurry.
Reduce the heat to medium and continue to whisk until the sauce thickens then remove from heat. Once the tofu and veggies have finished baking, drizzle them with 3/4 of the teriyaki sauce and serve hot.
Garnish with additional sauce if desired.