Preheat oven to 350°. Pulse ham in batches in a food processor until finely ground. Combine with the next 7 ingredients just until mixed. Shape into 1-in. balls; place in a single layer on greased 15x10x1-in. baking pans.
For glaze, cook and stir all ingredients in a small saucepan over medium heat until sugar is dissolved. Spoon over ham balls. Bake until ham balls are just beginning to brown, 30-35 minutes, rotating pans and carefully stirring halfway through. Gently toss in glaze. Serve warm.