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1
Adjust oven rack to lower-middle position, set large heatproof plate on rack, and heat oven to 200 degrees.
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2
Cut 1 lemon crosswise into slices 1/8 to 1/4 inch thick discarding ends; set aside.
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3
Juice the other lemon.
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4
Sprinkle both sides of chicken breasts generously with salt and pepper.
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5
Measure flour into pie tin or shallow baking dish.
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6
Coat chicken with flour, and shake to remove excess.
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7
Heat heavy-bottomed skillet over medium-high heat until hot, about 2 minutes.
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8
Add 2 TBSP oil and coat pan bottom.
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9
Lay half of chicken pieces in skillet.
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10
Saute without moving them, until lightly browned on first side, 2 to 2 1/2 minutes.
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11
Turn chicken and cook until second side is lightly browned, 2 to 2 1/2 minutes longer.
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12
Remove pan from heat and transfer chicken to plate in oven.
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13
Add remaining 2 tablespoons oil to now-empty skillet and heat until shimmering.
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14
Add remaining chicken pieces and repeat.
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15
Add garlic to now-empty skillet and return skillet to medium heat.
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16
Saute until fragrant, about 30 seconds for shallot or 10 seconds for garlic.
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17
Add stock and lemon slices, increase heat to high, and scrape skillet bottom with wooden spoon or spatula to loosen browned bits.
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18
Simmer until liquid reduces to about 1/3 cup, about 4 minutes.
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19
Add lemon juice and capers and simmer until sauce reduces again to 1/3 cup, about 1 minute.
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20
Remove pan from heat and swirl in butter until butter melts and thickens sauce; swirl in parsley.
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21
Spoon sauce over chicken and serve immediately.
