Pre-cook the green beans in boiling water until they are bright green and still very crisp, about 2 minutes; drain and set aside.
Heat the vegetable oil in a large saucepan over medium heat.
Add the sliced shallots and Thai green curry paste; cook, stirring, until the shallots soften, about 2 minutes.
Pour in the coconut milk and add the fish sauce and brown sugar; bring the mixture to a gentle boil.
Add the drained, cubed tofu, pre-cooked green beans, rehydrated shiitake mushrooms, and red bell pepper strips to the saucepan; stir and heat through for 3–5 minutes.
Stir in the chopped basil and fresh lime juice, then taste and adjust seasoning with salt and pepper as needed.
Divide the curry among bowls or serve over jasmine rice and garnish with basil sprigs and lime wedges.
