Position a rack in the center of the oven and heat the broiler.
Drizzle the kale with a little EVOO and season with salt, pepper and nutmeg. Arrange on a rack set over a rimmed baking sheet and broil until crisp, about 5 minutes.
Warm a serving platter in a 250°F oven.
Heat 1 tablespoon EVOO in a large skillet over medium-high heat. Sprinkle the fish with salt and pepper, then sauté until just cooked through, about 3 minutes on each side. Douse the fish with the vermouth, then transfer to the platter and cover to keep warm.
Return the skillet to the heat and toast the almonds over medium heat. Add the butter and cook until browned, about 3 minutes. Grate the zest of the lemon and add it to the browned butter, then squeeze in the juice from half the lemon. Stir in the parsley.
Arrange the fish on a bed of crispy kale. Slice the remaining lemon half into four thin rounds and place one on each piece of fish. Spoon the brown butter sauce and the almonds over top.