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In a shallow dish or bowl, combine 4 tablespoons flour, paprika, 1 teaspoon salt and pepper. Coat chicken breasts with the flour mixture.
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In a large skillet, brown the coated chicken in 1/4 cup of butter or margarine. Add the water, cover and let simmer covered for 25 to 30 minutes.
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Meanwhile, preheat oven to 350 degrees F (175 degrees C).
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When chicken breasts are done simmering, remove from the skillet and place in a 9x13 inch baking dish; save drippings. Combine remaining 2 tablespoons flour, 1/2 teaspoon salt and half-and-half. M.
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ix together and stir mixture into reserved drippings in skillet. Bring to a simmer, stirring, and cook until thick and bubbly.
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Add mushrooms and lemon juice and stir together. Pour sauce over chicken and bake uncovered in the preheated oven for 30 minutes.
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Sprinkle with cheese and bake 3-5 minutes more until cheese melts.