Prepare ingredients: drain the tofu well and cut into 1/2-inch cubes; trim the green beans and cut into 1″ pieces; slice the shallots; quarter the rehydrated shiitake mushrooms; cut the red bell pepper into strips; chop the basil and set aside a few sprigs for garnish; cut lime into wedges.
Bring a pot of water to a boil. Add the green beans and cook until bright green and still very crisp, about 1–2 minutes. Drain and transfer to a bowl of ice water to stop cooking, then drain again and set aside.
Heat 1 tablespoon vegetable oil in a large saucepan over medium heat. Add 3/4 cup sliced shallots and 1–2 tablespoons Thai green curry paste; stir and cook until the shallots soften and the paste is fragrant, about 2 minutes.
Add 1 14-ounce can unsweetened coconut milk, 2 teaspoons fish sauce, and 1 tablespoon brown sugar to the pan. Bring the mixture to a gentle boil.
Add the cubed tofu, the pre-cooked green beans, 5–6 rehydrated and quartered shiitake mushrooms, and 1 large red bell pepper (cut into strips). Stir and cook until everything is heated through and the vegetables are tender-crisp, about 3–5 minutes.
Remove the pan from the heat and stir in 1/4 cup chopped fresh basil and 2 tablespoons fresh lime juice.
Divide the curry among bowls. Garnish with basil sprigs and lime wedges before serving.