Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. Lightly grease the parchment with cooking spray or oil.

In a large mixing bowl, combine the shredded cheddar cheese, diced ham, flour, baking powder, garlic powder, onion powder, black pepper, and salt. Mix until well combined.

In a separate bowl, whisk together the egg and milk until smooth. Pour the egg mixture into the cheese and ham mixture, stirring until a dough forms.

Take small portions of the dough and roll them into sticks, about 3 inches long and 1 inch thick.

Place the breadcrumbs in a shallow dish. Roll each stick in the breadcrumbs until fully coated.

Arrange the coated sticks on the prepared baking sheet, leaving space between each one.

Bake in the preheated oven for 15-20 minutes, or until golden brown and crispy.

Remove from the oven and let cool for a few minutes before serving.