How to Make It
Blanch the kale in a large pot of salted water until limp, about 2 minutes. Drain well, pressing to extract excess water. In a small bowl, blend the flour and butter until smooth.
Heat 1 teaspoon of the oil in a large nonreactive skillet. Add the bacon and sauté over high heat until browned and crisp, about 4 minutes. Using a slotted spoon, transfer the bacon to paper towels to drain. Pour the rendered fat into a small bowl.
Heat 1 teaspoon of the oil and 1 teaspoon of the reserved bacon fat in the skillet. Separate the tenders from the chicken breasts. Season the chicken with salt and pepper. Add the breasts to the skillet and cook over moderately high heat until brown and crusty on the bottom, about 4 minutes. Turn and cook the other side until lightly browned, about 3 minutes. Brown the chicken tenders in another teaspoon of oil. Transfer the chicken to a platter and cover loosely with foil.
Heat 1 teaspoon of the oil and 1 teaspoon of the bacon fat in the skillet. Add the mushrooms, shallots and 2 tablespoons of water, season with salt and pepper and cook over moderate heat, stirring occasionally, until the vegetables are softened and browned, about 6 minutes. Transfer to a bowl and keep warm.
Pour the wine into the skillet and cook over high heat, scraping the bottom of the pan to loosen any browned bits, until reduced to a few tablespoons. Add the chicken stock and cook until reduced to 1/2 cup, about 3 minutes. Whisk in the flour paste and cook until the sauce thickens. Add the mushrooms and cook until warmed through. Transfer to a small bowl and stir in any accumulated juices from the chicken.
Wipe out the skillet and return it to high heat. Add the remaining 1 teaspoon oil and 1 more teaspoon of the bacon fat. Add the kale, season with salt and pepper and sauté until just beginning to brown, about 3 minutes. Stir in the reserved bacon and the lemon juice. Arrange the kale on 4 dinner plates. Top with the chicken breasts and mushroom sauce and serve.
Baked or mashed potatoes.