Place the tofu between two kitchen towels and press down lightly to remove excess water. Cut horizontally into three portions. Season with salt and pepper.
In a wide frying pan, heat enough vegetable cooking oil to reach a depth of one inch. Fry the tofu (side by side; do not overlap) on both sides until golden and crisp, about three minutes per side.
While the tofu cooks, make the stir fry. In a sauté pan, heat a tablespoonful of cooking oil.
Saute the onion and garlic until fragrant, about 30 seconds.
Add the Chinese broccoli stems to the pan, stir, sprinkle with salt and pepper. Cook for half a minute.
Pour in a generous splash rice wine. Allow to cook until the liquid has reduced to almost nothing.
Add the rest of the Chinese broccoli. Stir fry until limp.
Stir in the vegetarian oyster sauce and sesame seed oil to the starch solution. Pour into the pan. Stir quickly. Cook until the sauce is thick and clear.
Place a tofu steak on a plate, top with a third of the Chinese broccoli stir fry. Sprinkle with toasted sesame seeds. Do the same for the remaining tofu steak and stir fry.