Heat 2 teaspoons oil in small saucepan. Add onion, carrot and potato; sauté for 5 minutes or until slightly softened. Add broth; cover and cook 5 minutes.
Meanwhile, whisk together the flour, milk, parsley and salt in small bowl. Whisk flour mixture and 1/4 cup of the bread crumbs into the vegetable mixture in the saucepan. Cook for 2 minutes, whisking occasionally; the mixture will be thick. Remove from heat. Stir in ham and cheese. Refrigerate until cool to touch and scoopable in texture, about 30 minutes.
Whisk eggs in small bowl. Spread remaining bread crumbs in shallow dish. Using measuring tablespoon, scoop filling into 1-inch balls, rolling between hands coated with nonstick cooking spray. Dip croquettes into egg, then in bread crumbs to coat.
Heat frying oil in 8-inch skillet over medium-high heat. Working in batches, fry about 3 minutes per batch or until golden all around outside. Serve hot.