In a medium saucepan over medium heat, melt butter. Add onion and sauté until lightly browned.

Add rice and mix with a wooden spoon. Cook for about 3 minutes. Add in broth and parsley, and bring to a boil.

Reduce heat, cover and simmer for 30 minutes, or until all liquid is absorbed.

Remove from heat, and let cool for 30 minutes.

Stir in slightly beaten egg, cheddar cheese, parmesan cheese, and pepper into rice mixture. Pour breadcrumbs into a shallow bowl.

Moisten hands with water and shape into 14 balls, each about 1/4 cup of mixture. Roll each ball in bread crumbs. Moisten hands with water as needed, which will help prevent the rice from sticking to you.

Heat 2 TBSP of the vegetable oil in large skillet over medium heat. Add half of the croquettes, and cook on each side until lightly browned, about 4-5 minutes each. Remove carefully with a slotted spoon, and place on a plate lined with paper towels. Repeat this process with the second half of rice balls. [The balls may fall apart a bit when you flip them over or remove from the pan, but just reshaping them with a spatula or spoon worked for me.]

Place croquettes on a large plate and serve immediately.