Step 1

In a large skillet, melt the butter in the olive oil. Add the chicken, ham, nutmeg and a large pinch each of salt and pepper. Cook over moderate heat, stirring, for 3 minutes. Stir in 1/4 cup of the flour, then gradually whisk in 3/4 cup of the milk. Simmer for 3 minutes, stirring occasionally. Scrape the croquette mixture into a bowl; let cool. Cover and refrigerate until chilled, at least 1 hour.

Step 2

Divide the croquette mixture into 16 equal portions. Using wet hands, roll the portions into oval croquettes.

Step 3

Preheat the oven to 325°. In a shallow bowl, beat the eggs with the remaining 2 tablespoons of milk. Spread the bread crumbs and some flour in 2 more shallow bowls. Dredge each croquette first in the flour, then dip in the egg; coat the croquettes with bread crumbs and transfer to a platter.

Step 4

In a small saucepan, heat 1/2 inch of vegetable oil until shimmering. Fry 4 croquettes at a time, turning twice, until golden brown, about 3 minutes. Transfer the croquettes to a wire rack set over a baking sheet and keep warm in the oven while frying the rest. Serve immediately, with lemon wedges.