Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
Whisk together the soy sauce, sesame oil, garlic and ginger in a medium bowl until just combined. Set aside. Combine the rice, tofu and vegetables in a large bowl. Add the sauce and gently fold together with a rubber spatula until the rice is fully coated. Spread the mixture on the prepared baking sheet and cover with aluminum foil. Bake for 10 minutes. Remove the foil and bake until slightly browned, another 12 to 15 minutes. Garnish with the scallions and serve with hot sauce, if desired.