Remove the tofu from its packaging and place it on a plate lined with about 4 layers of paper towels; cover with more paper towels and set a heavy weight (or a cast-iron pan) on top to press out moisture. Let sit 30 minutes.
While the tofu presses, whisk together the hoisin sauce, soy sauce, sugar, grated ginger, minced garlic, and red pepper flakes in a medium bowl until combined.
Cut the pressed tofu into bite-sized pieces and add them to the bowl with the sauce; toss gently to coat and let marinate 30 minutes.
Heat the olive oil in a skillet or cast-iron pan over medium-high heat until hot. Add the tofu pieces in a single layer and sear without moving until bottoms are nicely browned, then flip and sear the other sides until golden and cooked through, about 6–8 minutes total.
Drizzle the sesame oil over the seared tofu, remove from heat, and transfer to a serving dish.
Sprinkle with sliced green onions and serve immediately with rice.