In a medium saucepan, melt the butter over medium-low heat. Whisk in 6 tablespoons flour and cook, whisking, for 1 minute. Gradually whisk in the milk, lower the heat and continue to whisk until the sauce thickens and turns glossy, 1 to 2 minutes. Stir in the thyme and nutmeg, then add the chicken and ham; season with salt and pepper. Refrigerate until firm, at least 2 hours or overnight.
Pour the remaining flour and the cornflakes onto separate plates. In a shallow bowl, beat the eggs. Shape heaping tablespoons of the chilled meat mixture into 2-by-1-inch cylinders and place on a parchment-paper- lined baking sheet. Coat each one with flour, dip into the eggs, then coat with the cornflakes; transfer to the baking sheet.
In a large skillet, heat the oil over medium-high heat. Working in batches, add the croquettes and fry until golden-brown, 2 to 3 minutes. Using a slotted spoon, transfer to paper towels to drain. Serve hot.