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1
Adjust oven rack to lower-middle position and heat up the broiler.
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2
Heat 1 tablespoon oil in large skillet over medium-high heat until just smoking.
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3
Add broccoli and cook until spotty brown, about 1 minute.
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4
Add 1/2 cup broth, cover, and steam until just tender, about 1 1/2 minutes.
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5
Remove lid and cook until liquid has evaporated, about 1 minute.
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6
Transfer broccoli to plate lined with paper towels; rinse and wipe out skillet.
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7
Heat remaining 2 tablespoons oil in now-empty skillet over medium-high heat until smoking.
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8
Meanwhile, season chicken with salt and pepper and dredge in flour to coat.
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9
Cook chicken until golden brown, 2 to 3 minutes per side.
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10
Transfer chicken to plate.
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11
With the heat off, add shallots to skillet and cook until just beginning to color, about 1 minute.
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12
Add remaining 2 cups broth and cream and scrape the bits from bottom of pan.
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13
Return chicken to skillet and simmer over medium heat until cooked through, about 10 minutes.
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14
Transfer chicken to clean plate and continue to simmer sauce until reduced to 1 cup, about ten minutes.
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15
Add sherry and Worcestershire and simmer until reduced again to one cup, about 3 minutes.
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16
Stir in 1 cup parmesan.
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17
Whisk egg yolks and lemon juice in a small bowl, then whisk in about 1/4 cup of the hot sauce.
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18
With the heat off, whisk egg yolk mixture back into the sauce in skillet, then whisk in the butter.
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19
Cut chicken into 1/2 inch thick slices and arrange on broiler-safe dish.
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20
Scatter broccoli over chicken, and pour sauce over broccoli.
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21
Sprinkle with remaining parmesan cheese and broil until golden brown, 3-5 minutes.
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22
Serve.
