Preheat the oven to 350 degrees . Spray 2 baking sheets with cooking spray. In a bowl, beat the eggs with a splash of water. On a plate, combine the bread crumbs and thyme. On another plate, combine the flour with a pinch each of salt and pepper. Lay 12 ham strips on a work surface. Top each with a cheese strip. Place a chicken chunk toward the end of each strip and roll up to enclose the chicken.
Working with 1 chicken nugget at a time, lightly coat with the flour, then the egg, then the bread crumbs. Transfer seam side down to the prepared baking sheets. Lightly spray the nuggets with cooking spray and bake until crisp, about 20 minutes.