In a medium nonstick skillet, cook the bacon over medium-high heat until crisp, about 5 minutes. Drain on paper towels, then finely chop.
In the same skillet, heat the oil over high heat. Add the rice and cook, stirring often, until warmed through, about 4 minutes. Add the cooked bacon and toss. Push the rice mixture to the side of the pan; add the egg to the pan and cook, stirring, until set, then stir into the rice. Transfer to a bowl, top with the cheddar and let cool. Sprinkle with the parsley.