Heat vegetable oil in a small skillet over medium-high heat. Add 1 Tbsp. chopped ginger and cook, stirring, until fragrant, about 1 minute. Transfer ginger to a small bowl; mix in soy sauce, lemon juice, sesame oil, and sugar. Set sauce aside.
Line a large steamer basket with scallion whites, cilantro stems, and sliced ginger. Set scallion greens and cilantro leaves aside.
Using a small knife, score skin side of fish at 1” intervals; season with salt and place in steamer, skin side up.
Set steamer in a large pot filled with 1” of simmering water and cover; steam fish until cooked through, 6–8 minutes.
Heat vegetable oil in a large skillet over medium-high heat. Add garlic and cook, stirring, until softened, about 1 minute.
Add kale, ½ tsp. salt, and ¼ cup water. Cover and cook, tossing occasionally, until leaves are tender and bright green, about 2 minutes.
Mix in kimchi, if desired, and sesame oil; season with salt and pepper.
Spoon sauce over fish, top with reserved scallion greens and cilantro leaves, and serve with sesame kale.