Press the tofu for about 10 minutes to remove excess water, then cut it into 1-inch cubes.
Place the sesame seeds in a dry skillet over medium heat and toast, stirring constantly, until golden and fragrant, about 2-3 minutes. Transfer to a small bowl.
Combine apricot jam, soy sauce, rice vinegar, and sesame oil in a small saucepan and warm over low heat, stirring until smooth and slightly thickened, about 2-3 minutes.
Heat the neutral oil in a non-stick skillet over medium-high heat until shimmering, around 180°C (355°F).
Add the tofu cubes to the skillet in a single layer, frying without moving for about 3 minutes until golden on the bottom. Flip and cook another 3 minutes until all sides are crispy.
Pour the warm apricot glaze over the crispy tofu in the skillet, gently tossing to coat evenly. Cook for another 1-2 minutes until the glaze is glossy and sticky.
Sprinkle the toasted sesame seeds over the glazed tofu, then turn off the heat and let sit for a minute to allow flavors to meld.
Serve the tofu hot, garnished with extra sesame seeds if desired, over steamed rice or greens for a complete meal.
