Make the rice cakes ahead, then reheat in the oven to free the stovetop for other items.
Melt butter in a large saucepan over medium-high heat. Add rice; cook 1 minute, stirring constantly. Add salt and broth; bring to a boil. Cover, reduce heat, and simmer 40 minutes or until liquid is absorbed, and rice is tender. Drain any excess liquid. Cool slightly.
Place egg and egg white in a large bowl; add flour and baking powder, stirring with a whisk. Add the rice, green onions, and next 4 ingredients (green onions through bacon), stirring with a rubber spatula until well blended.
Heat a large nonstick skillet coated with cooking spray over medium-high heat. Spoon 3 (1/4-cup) mounds rice mixture into skillet; flatten slightly with spatula. Cook 2 minutes on each side or until golden brown and thoroughly heated. Repeat procedure with remaining rice mixture. Serve immediately.