In a small bowl, mix together all the sauce ingredients.
Heat a large, non-stick skillet over medium-high heat. Add oil. Once hot, add tofu slabs in a single layer. Pan-fry tofu until lightly browned on each side, 3 to 4 minutes per side. Remove tofu from skillet and let cool for 5 minutes before slicing each slab into 1-inch (2.5-cm)-thick strips.
In the same skillet over medium heat, add the sauce and stir until the sugar dissolves. Increase heat to medium-high and bring sauce to a boil. Once boiling, lower heat to medium. Stir to prevent sugar from sticking and burning. Taste sauce and add more sugar, if desired.
Add sliced tofu to skillet, scoop sauce over tofu pieces. Continue to cook and baste tofu until it has absorbed some of the sauce, 6 to 7 minutes.
Increase heat to high and cook until sauce thickens, about 2 minutes. Remove from heat.
Garnish tofu with sesame seeds and scallions, if desired. Enjoy the Char Siu Tofu as is, with blanched veggies, with rice, or as filling for buns to make gua baos.