In a medium bowl or shallow plate, add soy sauce, sugar, vinegar, garlic sesame oil and ginger. Whisk to combine.
Crumble the tempeh into small chunks; place in the soy sauce mixture and stir to coat. Set aside.
In a medium skillet or wok over medium-low heat, warm olive oil. Add onion; stir. Cook for 5-7 minutes, until onion begins to brown. Add carrots and stir; cook for 3-5 more minutes, until carrot softens.
Pour the tempeh mixture into the pan; stir. Cook for 5 minutes, until tempeh starts to brown. Add tapioca starch; stir. Cook for 2-3 more minutes, stirring continuously, until sauce thickens.
Spoon the tempeh mixture into each lettuce cup. Top with sliced green onions and serve.