Season the tofu: Lightly sprinkle the tofu cubes with sea salt to enhance their flavor.
Sauté the aromatics: Heat the coconut oil in a large skillet (10- or 12-inch) over medium-high heat. Add the ginger, shallots, garlic, chile, and cilantro stems. Cook, stirring frequently, until softened and fragrant, about 5 minutes.
Cook the mushrooms and curry paste: Add the sliced shiitake mushrooms to the skillet and sauté until they become golden and tender, approximately 5 minutes. Season them with the ½ teaspoon of sea salt, then stir in the curry paste, cooking for 2 minutes to fully release its flavors.
Incorporate the liquids and seasoning: Pour in the coconut milk, making sure to scrape up any browned bits or curry paste from the skillet for extra flavor. Stir in the fish sauce, lime zest, and lime juice until well combined.
Add vegetables and simmer: Gently mix in the tofu cubes, green beans, and cherry tomatoes. Reduce the heat slightly and let everything simmer, stirring occasionally, until the sauce thickens a bit and the green beans are tender but still vibrant, about 7 to 10 minutes. Taste and adjust the seasoning by adding more fish sauce or salt if necessary.
Finish and serve: Transfer the curry to serving bowls and garnish with fresh basil or cilantro leaves for a fragrant, fresh finish.