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1
For Filling: Heat broiler.
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2
Toss asparagus with olive oil and season with salt and pepper; spread in single layer on pan and broil 4 inches from top heating element until tender and browned, 6 to 8 minutes, shaking pan to rotate spears halfway through cooking time.
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3
Sprinkle with balsamic vinegar; set aside.
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4
Heat unsalted butter in medium skillet over low heat until melted; add onion and saute, stirring occasionally,15 to 20 minutes.
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5
Stir in garlic and cook about 30 seconds longer; set aside.
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6
In medium bowl using hand mixer, beat cream cheese on medium speed about 1 minute.
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7
Stir in onion mixture, thyme, and Mozzarella; season with salt and pepper and set aside.
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8
For Chicken: Place each chicken breast on large sheet of plastic wrap, cover with second sheet of plastic wrap, and pound with meat pounder or rolling pin until 1/4-inch thick throughout.
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9
Each pounded breast should measure roughly 6 inches wide and 8-1/2 inches long.
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10
Place breasts skinned side down on work surface; season with salt and pepper.
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11
Fill, placing asparagus spears horizontally on top of cheese, spacing them about 1 inch apart, and trimming off ends if necessary.
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12
Roll and wrap each breast.
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13
Refrigerate until filling is firm, at least 45 minutes.
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14
Adjust oven rack to lower-middle position.
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15
Preheat oven to 400 degrees Fahrenheit.
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16
Spread flour in pie plate or shallow baking dish.
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17
Beat eggs with 1 tablespoon vegetable oil and 1 tablespoon water in second pie plate or shallow baking dish.
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18
Spread bread crumbs in third pie plate or shallow baking dish.
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19
Unwrap chicken breasts and roll in flour; shake off excess.
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20
Using tongs, roll breasts in egg mixture; let excess drip off.
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21
Transfer to bread crumbs; shake pan to roll breasts in crumbs, then press with fingers to help crumbs adhere.
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22
Place breaded chicken breasts on large wire rack set over jelly-roll pan.
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23
Heat remaining 3/4 cup oil in medium skillet over medium-high heat about 4 minutes; add chicken, seam side down, and cook until medium golden brown, about 2 minutes.
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24
Turn each roll and cook until medium golden brown on all sides, 2 to 3 minutes longer.
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25
Return chicken rolls, seam side down, to wire rack set over jelly-roll pan; bake until deep golden brown about 15 minutes.
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26
Let stand 5 minutes before slicing each roll crosswise diagonally into 5 medallions; arrange on individual dinner plates and serve.
