To prepare tofu, combine first 4 ingredients in a shallow dish. Combine breadcrumbs, flour, and sesame seeds in a shallow dish.
Dip tofu, one piece at a time, in egg mixture; dredge in breadcrumb mixture. Return tofu to egg mixture; dredge in breadcrumb mixture. Repeat procedure with remaining tofu, egg mixture, and breadcrumb mixture.
Heat 1 tablespoon oil in large nonstick skillet over medium-high heat. Add half of tofu; cook 4 minutes, turning to brown all sides. Remove from pan. Repeat procedure with remaining oil and tofu. Keep warm.
To prepare vegetables, pour pineapple juice into pan. Bring to a boil; cook until juice is reduced to 1/4 cup (about 5 minutes). Remove from pan.
Heat pan coated with cooking spray over medium-high heat. Add shallots, minced garlic, and mushrooms; sauté 4 minutes, stirring occasionally. Add green onions, tomatoes, and thyme, and cook 1 minute. Stir in pineapple juice and balsamic vinegar, and cook 30 seconds.
Arrange about 1/2 cup vegetable mixture on each of 6 plates; top each serving with 3 tofu sticks. Drizzle with 1/2 teaspoon sweet and sour sauce, if desired. Serve immediately.