Boil shallots, vinegar, and wine in a saucepan until only 30ml of liquid remains.
Add 15ml of cold water and simmer until 15ml remains.
Whisk in the butter gradually over low heat until fully incorporated.
Strain the mixture, then stir in seasoning, crab, tomatoes, chives, and lemon juice.
Blanch kale in boiling water for 2 minutes, then refresh in ice water and dry.
Melt butter in a pan and sauté the kale until wilted.
Season kale with lemon juice, salt, and pepper.
Season lemon sole fillets with salt and pepper.
Fry the fish in butter for 2 minutes on each side.
Serve fish on a bed of kale and top with crab butter sauce.