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1
Heat the butter and oil in a medium saucepan over medium heat until the butter has melted.
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2
Add the onion; season with salt and pepper.
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3
Cook, stirring occasionally, until the onion is translucent, about 3 minutes.
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4
Add the flour; cook, stirring, 1 minute.
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5
Whisk in the milk, and cook, whisking, 3 minutes.
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6
Whisk in the ham and 1/3 cup cheese.
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7
Season with salt and pepper as desired.
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8
Spread the mixture onto a baking sheet, and let cool completely.
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9
The mixture can be refrigerated in an airtight container up to 2 days.
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10
Whisk together the eggs in a shallow dish.
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11
Stir together the bread crumbs and remaining 1/4 cup cheese in another shallow dish.
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12
Scoop tablespoons of the cooled mixture, and shape with floured hands into 2-inch ovals.
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13
Working with 1 oval at a time, coat in the beaten egg, then in the bread crumb mixture.
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14
Transfer to a parchment-lined baking sheet.
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15
Heat 2 1/2 inches oil in a large, heavy stockpot until it registers 375F on a deep-fry thermometer.
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16
Working in batches to avoid crowding, fry the croquettes, flipping once, until dark golden brown, 1 to 2 minutes total.
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17
Using a slotted spoon, transfer to paper towels to drain.
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18
(Adjust the heat between batches as needed to keep oil at a steady temperature.)
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19
Serve warm, garnished with parsley sprigs.
