With a knife, trim edges of the bread and with a rolling pin, flatten until very thin.
Spread a thin layer of jam on the top side of the bread slice.
Arrange a piece of ham over the jam and place cheese strip at the edge of the bread.
Roll bread into a log to enclose filling and press lightly on seams to completely seal. Secure with toothpicks, if needed, and remove when ready to dredge in bread crumbs.
Repeat with remaining bread slices.
In a bowl, combine eggs and milk and whisk together until well-beaten. In a shallow dish, combine bread crumbs and Italian seasoning.
Dip bread rolls in egg mixture and roll in bread mixture, patting down crumbs to fully coat.
In a wide, thick-bottomed pan over medium heat, heat about 2-inches deep of oil. Carefully place breaded rolls seam side down and fry, turning on sides as needed, until golden and crunchy.
Remove from pan and drain on a wire rack set over a baking sheet. Serve hot.