Heat a wok or large skillet over medium-high heat and add sesame oil; cook and stir ground beef until browned and crumbly, 5 to 7 minutes. Add kimchi; cook and stir for 10 minutes. Add rice; cook and stir until heated through, about 5 minutes.
Move the fried rice to 1 side of wok. Crack eggs into wok and cook until bottoms are set, 2 to 3 minutes. Flip eggs and cook until set, 2 to 3 minutes. Serve 1 egg on top of each fried rice portion.