Preheat your oven to 200°C (390°F). Line a baking sheet with parchment or a silicone mat.
Drain and press the tofu to remove excess moisture, then cut it into 1-inch cubes. Toss the tofu gently with 1 tablespoon of neutral oil to coat evenly.
Spread the tofu cubes on the prepared baking sheet in a single layer. Bake for 20 minutes, flipping halfway through, until edges are golden and crispy.
While the tofu bakes, combine the apricot jam, soy sauce, grated ginger, and a splash of lemon juice in a small saucepan. Bring to a gentle simmer over low heat, stirring occasionally, until the mixture is glossy and slightly thickened, about 5 minutes.
Heat a dry skillet over medium-low heat and toast the sesame seeds until fragrant and golden, about 2-3 minutes. Remove from heat and set aside.
Once the tofu is crispy and baked, transfer it to the skillet with the warm apricot glaze. Gently toss to coat each piece evenly and cook for another 2 minutes until the glaze is sticky and glossy.
Remove the glazed tofu from heat and let it rest for 2 minutes to allow the glaze to set slightly.
Transfer the tofu to a serving bowl and sprinkle with toasted sesame seeds and sliced green onions. Serve immediately, perhaps with rice or greens on the side.