Press the tofu: place the tofu between paper towels and press for about 10 minutes to remove excess water. Once pressed, cut into evenly sized cubes.
Heat your skillet over medium-high heat and add 1 tablespoon of neutral oil. When shimmering and aromatic, carefully add the tofu cubes in a single layer. Cook for 4-5 minutes without moving, then flip gently with a spatula. Continue cooking, turning occasionally, until all sides are golden and crispy, about 10 minutes total.
While the tofu crisps up, toast the sesame seeds in a dry pan over medium heat. Shake the pan frequently, and remove them once they turn golden and fragrant, about 2 minutes.
In a small bowl, stir together the apricot jam, rice vinegar, and soy sauce to create a glossy glaze. Mix until smooth and set aside.
Once the tofu is crispy and golden, remove it from the skillet and toss gently with half of the apricot glaze to coat evenly. This allows the glaze to set quickly, creating a sticky, flavorful coating.
Arrange a bed of thinly sliced cucumber and shredded carrot on your serving plates. Place the glazed tofu on top, then sprinkle generously with toasted sesame seeds for crunch and aroma.
Drizzle the remaining apricot glaze over the assembled bowls for extra shine and flavor. Finish with additional sesame seeds if desired. Serve immediately to enjoy the crispy tofu and fresh vegetables at their best.