Melt the butter in a small saucepan over medium heat.

Add the flour and cook, stirring constantly, for about 3 minutes.

Gradually stir in the milk, salt, black pepper, and nutmeg.

Cook, stirring constantly, until thickened and smooth.

Spread the mixture out on a dinner plate and let it cool.

Refrigerate until firm enough to handle (about 1 hour).

Shape the cheese mixture into 1¼-inch balls.

Place the eggs and flour in separate shallow bowls.

Heat at least 1 inch of oil in a large skillet over medium-high heat (or use a deep fryer set at 365°F) until it turns a cube of bread light brown in 60 seconds.

Dip each croquette in the beaten egg, dredge in the bread crumbs, and place in the hot oil.

Cook, turning several times, until golden.

Transfer the croquettes with a slotted spoon to paper towels and let them drain.

Serve hot.