Stick the dried mushrooms in heatproof bowl and cover with the boiling water. Place a paper towel directly onto the top of the water, covering the whole top of bowl, to keep the mushrooms submerged. Let sit until rehydrated, about 10 minutes.
Meanwhile, heat 2 tablespoons canola oil in a pan. Add button mushrooms and fry, stirring often, until well browned, 6 to 10 minutes. Set aside.
Whisk together vegetable broth, bean paste, and soy sauce. Set aside.
Retrieve rehydrated 'shrooms! Drain well, removing any stemmy or super-tough bits. Give them a rough chop and then add to the fried 'shrooms pile.
Heat remaining 3 tablespoons canola oil in a large sauté pan over medium heat. Add garlic and ginger, pushing the mess around for a minute or two with a wooden spoon, until fragrant. Add the cubed tofu and vegetable broth mixture, and then simmer for another one to two minutes.
Add corn starch and cook for another minute, while the sauce bubbles and thickens. Stir in mushrooms.
Remove pan from heat, and stir in the sesame oil. Scoop a big ol' heap of the tofu/mushroom/saucy mixture over a bowl of rice, then top with a sprinkling of scallions.