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1
Adjust oven rack to middle position and heat oven to 400 degrees.
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2
Using kitchen shears, remove any rib bones that extend beyond each breast.
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3
Working with 1 breast at a time, place skin side down on counter with breast side facing your knife hand.
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4
Pres on breast with your opposite hand to flatten slightly and, using sharp paring knife, cut 3-inch-long horizontal pocket in the side of the breast, stopping 1/2 inch from end so halves remain attached.
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5
Using your fingers and tip of knife, make interior of pocket wider without increasing 3-inch opening.
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6
Season breasts inside and out with salt and pepper; set aside.
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7
Heat 1 tablespoon oil in 12 inch oven safe nonstick skillet over medium heat until shimmering.
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8
Add onion and 1/8 teaspoon salt and cook until softened and browned around edges, 4-6 minutes.
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9
Remove from heat and set aside to cool slightly, about 5 minutes.
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10
Combine lemon juice, garlic, thyme, mustard, rosemary, and 2 tablespoons oil in bowl; set aside 2 teaspoons oil mixture for sauce.
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11
Stir salami, Parmesan, capers, onion, 1 tsp pepper, and 1/4 tsp salt into remaining oil mixture, mashing against side of bowl with back of spoon until stuffing mixture clumps together.
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12
Place about 3 tablespoons stuffing mixture into pocket of each breast, pressing into ends of pockets with your fingers to fill completely and evenly.
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13
Fold breast over to enclose.
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14
Secure each breast with 3 evenly spaced pieces of kitchen twine.
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15
Wipe skillet clean with paper towels.
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16
Bake chicken breasts with broth (optional).
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17
Bake until the thickest part of stuffing registers 160 degrees, 30 -37 minutes.
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18
Transfer breasts to carving board, tent with aluminum foil, and let rest for 15 minutes.
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19
Meanwhile, pour pan juices into liquid measuring cup and skim off fat.
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20
Stir in lemon juice and reserved oil mixture; season with salt and pepper to taste.
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21
Slice chicken breasts 1/2 inch thick, transfer to serving platter and drizzle with sauce.
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22
Serve.
