In a medium-size saucepan over high heat, bring the chicken broth to a boil and add the rice. Reduce the heat and simmer, uncovered, until the rice is tender, about 16-18 minutes. Transfer to a medium bowl and let cool.
While the rice is cooking, in a medium-size, nonstick skillet, cook the bacon over medium-high heat until crisp, about 4 minutes. Remove the bacon from the pan, reserving the bacon fat to cook the rice cakes.
Finely chop the bacon and add it to the cooled rice. Mix in the egg and breadcrumbs, and season with salt and freshly ground black pepper. Combine thoroughly and score the mixture to make 4 equal-size portions. Wet your hands before forming the portions into thin cakes so the rice doesn't stick to you.