Whisk first 6 ingredients in a medium bowl. Add beef; toss to coat. Cover; chill for 30 minutes or up to 3 hours.
Heat 1 tablespoon oil in a large cast-iron or nonstick skillet over medium heat. Add rice; pat out in an even layer. Cook, rotating skillet for even browning (do not stir), until rice is golden and crisp on bottom, about 15 minutes.
Meanwhile, heat 1/2 tablespoon oil in a large heavy skillet over medium heat. Add one-quarter of beef and cook, turning once, until cooked through and lightly browned, about 3 minutes. Transfer to a bowl. Repeat in 3 batches with remaining oil and beef.
Divide rice among bowls. Top with beef, Bibimbap Mix-Ins, and eggs. Serve kimchi alongside.
