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1
Prepare the eggs: Bring a large saucepan of water to a simmer over medium-high heat.
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2
Add 4 eggs and simmer 5 minutes for very runny yolks, or 6 minutes for yolks that are slightly set around the edges.
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3
Transfer the eggs to a bowl of ice water with a slotted spoon; drain, peel carefully and pat dry.
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4
Season with salt.
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5
Put the flour in a shallow dish and season with salt and pepper.
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6
Put the breadcrumbs in another dish; season with salt and pepper.
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7
Beat the remaining 2 eggs in a third dish; season with salt and pepper.
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8
One at a time, carefully dredge the cooked eggs in flour, then roll in the beaten eggs, letting the excess drip off, and roll in the breadcrumbs.
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9
Roll in the beaten eggs again and reroll in the breadcrumbs.
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10
Put the eggs on a parchment-lined plate; refrigerate while you make the gravy.
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11
Reserve 2 tablespoons of the seasoned flour.
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12
Make the gravy: Heat the olive oil in a medium skillet over medium heat.
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13
Crumble the sausage into the skillet and cook, breaking it up with a wooden spoon, until browned, 3 to 4 minutes.
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14
Add the thyme and the reserved 2 tablespoons seasoned flour and cook, stirring, 1 minute.
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15
Stir in the chicken broth and cream and bring to a simmer.
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16
Cook, stirring occasionally, until the gravy thickens, 4 to 5 minutes.
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17
Stir in the parsley and season with salt and pepper.
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18
Add more cream or water if the gravy is too thick.
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19
Keep warm.
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20
Deep-fry the eggs: Heat about 2 inches of vegetable oil in a medium saucepan over medium heat until a deep-fry thermometer registers 375 degrees F. Using a slotted spoon, carefully lower the breaded eggs into the hot oil and fry, turning, until golden brown, about 2 minutes.
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21
Drain on paper towels.
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22
Serve the gravy and fried eggs on the biscuits.
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23
Photograph by James Wojcik
