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.

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

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

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.