Preheat the oven to 350F. Spray 2 baking sheets with nonstick cooking spray.

Place the eggs in a shallow bowl and beat lightly with a splash of water. Place the breadcrumbs and thyme in another shallow bowl. Place the flour in a third shallow bowl and season liberally with salt and pepper.

Cut the ham and the cheese into strips about 1 to 1 1/2 inches wide. (Cut them lengthwise so they are long - you should be able to get 3 to 4 strips from each piece of ham, and 3 from each slice of cheese.)

On a work surface, place one piece of cheese on top of one of the strips of ham. Place a chunk of chicken on one end and roll up to enclose the chicken. Working with one at a time, lightly coat with the flour, then dunk in the egg then roll in the breadcrumbs. Place on the baking sheet, seam side down. Continue with the rest of the nuggets.

Bake until the chicken is cooked through and the nuggets are golden, about 20 minutes.