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1
Preheat the oven to 250 F. Heat the 3 tablespoons of the olive oil and 4 tablespoons of the butter in a large, heavy skillet over medium-high heat until the butter is foaming.
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2
Meanwhile, season the fillets with salt and pepper and dredge them in the flour to coat both sides lightly.
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3
Gently lay as many of the fillets into the pan as fit without touching.
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4
Cook just until the underside is lightly browned, about 4 minutes.
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5
Flip them gently with a wide metal spatula and cook until the second side is browned and the fish is opaque in the center, about 2 minutes.
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6
Transfer them with the spatula to a baking sheet and keep them warm in the oven.
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7
Repeat if necessary with the remaining fillets, adjusting the heat under the skillet to prevent the bits of flour in the pan from burning.
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8
When all the sole fillets have been browned, carefully wipe out the skillet with a wad of paper towels.
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9
Add the remaining 2 tablespoons olive oil and the remaining 2 tablespoons butter and return to medium heat.
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10
When the butter is foaming, slide in the lemon slices and garlic and cook, stirring gently, until the lemon slices are sizzling and lightly browned.
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11
Remove the lemon slices and set them aside.
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12
Stir in the capers and heat until they are sizzling, about 1 minute.
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13
Pour in the lemon juice and wine, bring to a boil, and cook until reduced by about half.
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14
Pour in the vegetable stock, bring to a boil, and boil until the sauce is lightly thickened, about 2 minutes.
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15
If you like, drizzle in a tablespoon or two of olive oil to enrich the sauce.
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16
Sprinkle in the parsley and taste, seasoning with salt and pepper if you like.
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17
Remove the sole from the oven and set 1 fillet in the center of each plate.
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18
Top each fillet with 2 of the lemon slices.
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19
Spoon the sauce around the fillets, dividing it evenly.
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20
Serve immediately.
