Rinse the rice in a fine-mesh sieve under cold water for about 10 seconds, stirring the rice with your fingers, then drain well. Transfer the rice to a small pot and add the 1 1/2 cups water. Bring to a simmer over medium-high heat, then cover and reduce the heat to low. Cook for 12 minutes. Remove from the heat and let the rice sit, covered, for 10 minutes.
Drain the tofu and cut it lengthwise in half, then into ½-inch-thick slices. Line a small baking sheet with paper towels or a clean kitchen towel and arrange the tofu on top. Cover with another towel and blot the tofu dry, removing as much excess moisture as possible.
Cut the thicker broccolini into 3- to 4-inch pieces diagonally. Mince the garlic and ginger, and thinly slice the red onion. In a small bowl, whisk together the soy sauce, oyster sauce, brown sugar, Shaoxing wine or water, and chili flakes.
Heat the vegetable oil in a large skillet over medium heat, and add a pinch of salt. Arrange the tofu in a single layer and increase the heat to medium-high. Cook until the underside is golden brown and the tofu releases easily from the pan, for 4 to 5 minutes. Flip and cook until the other side is golden brown, another 4 to 5 minutes. Transfer the tofu to a plate.
Add a little more oil to the skillet if the pan is dry. Add the broccolini and cook for about 3 minutes, until lightly charred and just tender. Add the ginger, garlic, and red onion and cook for about 30 seconds, until fragrant. Add the sauce and cook for about 1 minute, until slightly reduced. Return the tofu to the pan and toss gently to coat with the sauce. Serve over rice and garnish with toasted sesame seeds.