Slice the tenderloin (the small flap of meat) from chicken breast halves; set aside. Cut each breast on the bias into 3 medallions. Place tenderloins and medallions between 2 layers of plastic wrap and pound to 1/16 inch thick. On each piece, layer a slice of fontina, half a slice of prosciutto, and a sage leaf; secure by threading a toothpick through the layers. Sprinkle underside of each with salt and pepper.
Melt 1 tablespoon butter in a skillet over high heat. Saute half the pieces, chicken side down, until golden, 2 to 3 minutes. Turn and cook 1 minute more. Remove from pan and keep warm. Repeat with 1 tablespoon butter and remaining chicken. Remove and keep warm.
Pour Madeira into skillet and let reduce slightly, about 1 minute. Add remaining 1 tablespoon butter and cook, swirling pan, until sauce thickens, about 30 seconds. Pour sauce over chicken, remove toothpicks, and serve immediately.
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