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1
To butterfly and stuff chicken breasts: If tenders are attached to undersides of breast halves, remove white tendons from tenders with a small sharp knife.
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2
Working with 1 at a time, butterfly breast halves: Lay each breast half, skinned side up, lengthwise on a cutting board.
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3
Holding a sharp knife parallel to work surface and beginning on a long side, cut breast almost in half horizontally (not all the way through), then open it like a book.
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4
Cover opened breast halves with a piece of plastic wrap and gently pound each to an even 1/2-inch thickness with a meat pounder or rolling pin.
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5
Remove plastic wrap and cover each opened breast half with 1 slice of ham and 1 slice of cheese, tucking in any protruding ends.
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6
Brush edge of chicken with some egg, reserving remainder, then fold each breast in half to enclose ham and cheese.
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7
To cook chicken and make sauce: Pat chicken dry and sprinkle with salt and pepper.
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8
Heat 2 tablespoons butter in a 12-inch heavy skillet over moderately high heat until foam subsides.
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9
While butter is heating, quickly brush more egg onto seam of each breast again, then dredge breasts in flour, shaking off excess.
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10
Saute chicken, turning over once, until golden and cooked through, about 8 minutes total.
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11
Transfer to a plate and keep warm, loosely covered with foil.
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12
Add remaining tablespoon butter to skillet, then saute mushrooms and shallot, stirring, 1 minute.
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13
Add wine and deglaze skillet by boiling, stirring and scraping up brown bits, until wine is reduced by about half, 1 to 2 minutes.
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14
Add tomatoes and cook, stirring occasionally, until they begin to soften, 3 to 4 minutes.
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15
Add cream and simmer, stirring occasionally, until reduced by about half, about 6 minutes.
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16
Stir in any chicken juices accumulated on plate and season sauce with salt and pepper.
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17
Serve chicken topped with sauce.
