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1.
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Preheat oven to 350 degrees F. Brush a rimmed baking pan with a light coating of olive oil.
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2.
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Prepare a breading assembly line by putting 1/4 cup of flour in the first of 3 wide, shallow bowls.
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Put the beaten eggs in the second.
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Melt 2 tablespoons of unsalted butter in the third bowl (heat it in the microwave for 30 seconds or until melted) and mix in 3 cloves of roasted garlic, the herbs de Provence, 1 teaspoon of kosher salt and 1/2 teaspoon of freshly ground black pepper to form a loose paste.
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Add the panko breadcrumbs and stir to combine and there are no lumps in the fluffy breadcrumbs.
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Set aside.
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3.
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Slip two chicken breasts, side by side, into a gallon size zipper storage bag and pound them to about 1/4 thickness.
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Remove them from the bag and set aside on a plate.
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Repeat with remaining two breasts.
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4.
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Stretch a sheet of plastic wrap on the work surface and place a single, flattened, chicken breast on top.
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Center a slice of prosciutto on the chicken and spread 1/4 of the shredded smoked Gruyere over the slice of ham.
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5.
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Starting at the longest end, roll the chicken breast up like a jelly roll and roll the plastic wrap tightly around the chicken.
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Repeat with the remaining 3 chicken breasts.
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6.
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Remove the chicken roulades from the plastic wrap and dredge in the flour, brushing off the excess.
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Then dip the flour dredged chicken into the beaten eggs to cover completely and then roll them gently in the panko mixture.
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Place the roulades, seam side down, in the prepared baking pan and bake for 45 minutes.
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7.
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During the last 15 minutes of baking time, prepare the white sauce by melting 2 tablespoons of unsalted butter in a saute pan over medium heat.
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When the butter is bubbling add 1 1/2 tablespoons flour and stir to combine.
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Cook the butter and flour for 4 minutes then mash in the remaining roasted garlic and the white pepper and cook, stirring for 1 minute.
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Remove from heat and slowly whisk in the milk until completely incorporated.
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Return the pan to the heat and bring to simmer stirring occasionally until thickened.
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Remove from heat, stir in the remaining 2 tablespoons of butter until thoroughly blended and cover until ready to serve.
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Remove the roulades from the oven and let them rest for 5 minutes.
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Slice each into 1/2 to 3/4 thick slices and serve placed in a pool of the roasted garlic white sauce.
