Place eggs in a large saucepan. Cover with water to 1 inch above eggs; bring just to a boil. Remove from heat; cover and let stand 12 minutes. Drain and rinse with cold running water until cool.
Peel eggs; slice in half lengthwise. Remove yolks; discard 4 yolks. Place remaining 4 yolks in a medium bowl. Add ham and next 7 ingredients (through pepper); stir until combined.
Place bread in a food processor; pulse 10 times or until coarse crumbs measure 1 cup.
Spoon about 1 teaspoon yolk mixture into each egg white half. Top each half with 1 tablespoon breadcrumbs. Coat breadcrumbs with cooking spray.
Place eggs on a baking sheet; broil 1 minute or until breadcrumbs are toasted. Garnish with thyme leaves, if desired.