Step 1

Let 1 1/2 cups whole milk sit at room temperature about 30 minutes. Meanwhile, finely dice 1/2 small yellow onion. Finely dice 4 ounces ham.

Step 2

Melt 4 tablespoons unsalted butter in a medium saucepan over medium heat. Add the onion and cook, stirring occasionally, until just softened, about 3 minutes. Add 1/2 cup all-purpose flour and cook, stirring constantly, about 2 minutes. While stirring constantly, very slowly pour in the milk. Add 1 teaspoon kosher salt and a pinch ground nutmeg, and stir until smooth. Add the ham and cook, stirring constantly, until the dough thickens and dries out slightly, about 2 minutes.

Step 3

Transfer the dough to a bowl. Let cool for 30 minutes. Cover and refrigerate until chilled, at least 2 hours, preferably overnight.

Step 4

Place 1 cup plain, fine bread crumbs in a shallow dish. Lightly whisk 1 large egg in a second shallow dish.

Step 5

Line a large plate or rimmed baking sheet with parchment paper. Scoop 2 tablespoons dough and roll to form a 2-inch log. Place on the prepared plate or baking sheet and repeat with the remaining dough.

Step 6

Working with 1 log at a time, dip in the beaten egg until coated and let any excess drip off. Dredge in the bread crumbs, gently pressing them in to adhere. Return to the plate and repeat with the remainder of the logs. Feeze at least 15 minutes. Meanwhile, heat the oil.

Step 7

Heat 1/2-inch vegetable oil (about 3 cups) in a Dutch oven or other heavy-bottom pot over medium heat to 375ºF. Line a large plate with paper towels.

Step 8

Frying in batches of 6, add the croquetas to the oil and fry, flipping halfway through, until golden-brown all over, 2 to 4 minutes total. Using a slotted spoon, transfer the croquetas to the plate to drain. Serve immediately.