Heat 1 tablespoon of sesame oil in a large skillet over medium-high heat. Add the tofu cubes and cook for 8 to 10 minutes, turning occasionally until golden on all sides. Remove the tofu from the skillet and set it aside.
Add the remaining tablespoon of sesame oil to the same skillet. Stir in the garlic and ginger, then cook for 30 seconds until fragrant.
Add the broccoli florets and cook for 4 to 5 minutes, stirring often, until they turn bright green and start to soften.
Return the tofu to the skillet. Pour in the soy sauce and stir everything together. Cook for 2 more minutes to let the flavors combine.
In a separate pan, lightly sauté the zucchini noodles over medium heat for 2 to 3 minutes until just warmed. Do not overcook them.
Divide the zucchini noodles among four plates. Spoon the tofu and broccoli mixture on top. Finish with sliced green onions and sesame seeds.