Cook the rice in a pot or rice cooker, per directions on the package. Remove from rice cooker and layer on flat baking sheet. Cover and allow to cool completely. Refrigerate until needed.
Remove rice from refrigerator and scoop into large bowl. Set aside to return to room temperature. Keep covered.
Mix together the soy sauce, rice vinegar, and 1 tbsp sesame oil. Set aside.
In a large bowl, fill with ice and water. Set aside. Drain the tofu.
In a hot skillet, toast the sesame seeds and set aside. Start a large saucepan filled with heavily salted water to a rolling boil.
Trim the bottoms of the mushrooms clusters and separate. Saute the mushrooms in 2 tbsp of sesame oil, salt to taste. Stir occasionally until mushrooms are well browned. Remove from heat.
While mushrooms are sauteing, cut broccoli into bite sized pieces and blanch in the hot salted water. Shock broccoli in ice water. Gently wring to dry, then mix with 1 tsp sesame oil and salt to taste. Set aside.
Cut the tofu into 4 large triangles or cubes as desired. Roll the tofu in the cornstarch or flour.
Heat large pan and add oil for deep frying. When the oil is heated to at least 350 degrees F, carefully add 2 tofu pieces into the pan.
Fry, stirring occasionally, until the tofu is golden on both sides. Remove with a slotted spoon and drain on paper towels. Keep warm while frying the remaining tofu.
Shake the dressing vigorously and mix about half into the rice. Add more to taste. The rice should be well-coated but not sopping wet. Fold in the toasted sesame seeds.
Spoon out the avocados and cut into 1/2 inch chunks. Season with salt.
Fold the diced avocados into the rice and transfer the rice into serving bowls. Top with broccoli rabe, beech mushrooms and deep fried tofu. Garnish with additional untoasted sesame seeds.