Wrap tofu in two layers of paper towels and place on a plate. Put another plate on top of the tofu to weigh it down, and microwave for 2-3 minutes, or until drained.
After microwaving, carefully unwrap tofu and slice into ½-1 inch cubes. Pat each cube dry.
In a large nonstick skillet, heat vegetable oil and 1 teaspoon of sesame oil over medium-high heat. Once the oil is hot, add cubes of tofu and cook on all sides until golden brown, approximately 2-4 minutes per side, then remove from pan and set aside.
Add broccoli to the hot pan and add vegetable broth. Cover with a lid and reduce heat to medium-low. Steam for 5 minutes.
Remove lid and turn heat back up to medium-high.
Add garlic, grated ginger, and ½ teaspoon sesame oil. Stir to soften.
Add in soy sauce, agave, sesame seeds, and cornstarch slurry. Stir until thickened to desired consistency.
Add tofu back into broccoli and sauce mixture.
Serve over white rice and garnish with green onion and sesame seeds.