In a skillet, toast the green peppercorns over moderately high heat until fragrant, about 30 seconds. Transfer to a spice grinder and let cool completely; coarsely grind.

Using poultry shears, remove the backbones and wingtips from the hens and reserve for another use. Remove the legs and separate them into drumsticks and thighs. Remove the whole breasts on the bone and split each breast down the center. (A butcher can do this for you.)

Season the hen pieces with salt and black pepper. In a large pot, heat the oil until shimmering. Add half of the hen pieces and cook over high heat, turning once, until browned, about 4 minutes; transfer to a plate. Repeat with the remaining hen pieces.

Add the chiles, shallots, garlic, ginger, lemongrass, and turmeric to the pot and cook, stirring, until fragrant, 1 minute. Add the water and kohlrabi. Return the browned hen pieces to the pot and bring to a boil. Cover and simmer until the breast meat is just cooked through, 15 minutes. Transfer the breast pieces to a plate and cover. Simmer the stew until the legs and thighs are just cooked through, 10 minutes longer.

Return the breast pieces to the stew and reheat. Stir in the ground green peppercorns, fish sauce, scallions, lime zest, and cilantro. Ladle the stew into bowls and serve.