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1
Place each chicken breast on large sheet of wax paper, cover with second sheet, and pound with meat pounder or rolling pin until 1/4-inch thick throughout. Each pounded breast should measure roughly 6 inches wide and 8 inches long. Cover and refrigerate while preparing filling.
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2
For filling, heat butter in medium skillet over low heat until melted; add onion and saute, stirring occasionally, until deep golden brown, 15 to 20 minutes. Stir in garlic and cook until fragrant, about 30 seconds longer; set aside. In medium bowl, beat cream cheese on medium speed until light and fluffy, about 1 minute. Stir in onion mixture, gorgonzola, almonds, figs, season with salt and pepper and set aside.
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3
Place breasts on work surface; season with salt and pepper. Spoon filling into center of chicken, roll, and wrap each breast. Refrigerate until ready to cook.
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4
Adjust oven rack to lower-middle position; heat oven to 400 degrees. Beat eggs with 1 tablespoon vegetable oil and 1 tablespoon water in second pie plate or shallow baking dish. Spread bread crumbs in separate pie plate or shallow baking dish. With tongs, dip rolled chicken breasts in egg mixture; let excess drip off. Transfer to bread crumbs; shake pan to roll breasts in crumbs, then press with fingers to help crumbs adhere. Place breaded chicken breasts on large wire rack set over jelly-roll pan.
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5
Heat remaining oil in medium skillet over medium-high heat until shimmering, but not smoking, about 4 minutes; add chicken, seam side down, and cook until medium golden brown, about 2 minutes. Turn each roll and cook until medium golden brown on all sides, 2 to 3 minutes longer. Return chicken rolls, seam side down, to wire rack set over jelly-roll pan; bake until deep golden brown about 15 minutes. Let stand 5 minutes before slicing each roll crosswise diagonally into 5 medallions; arrange on individual dinner plates and serve.
