Mix the soy sauce, maple syrup, and red pepper flakes in a shallow baking dish. Add the pork and turn to coat evenly. Let stand until ready to cook. While the pork marinates, halve and thinly slice the shallot.
Remove the pork from the marinade, wiping off excess. Reserve the marinade. Lightly season the pork with salt on both sides. Heat the oil in a large skillet over medium heat. Add the pork and cook, turning once, until browned and barely pink in the center, about 12 minutes. Transfer the pork to a cutting board.
To the same skillet, add the shallots and stir well. Add the broccoli, a generous pinch of salt, and 1/4 cup water. Stir and scrape up all the browned bits from the pan, then spread the broccoli in an even layer. Cover and cook until the broccoli is bright green and crisp-tender, 2 to 3 minutes.
Uncover, add the reserved marinade, and bring to a boil. Add the kimchi and stir until heated through, about 1 minute. Divide among 4 serving plates.
Place each pork chop on a plate, drizzling any accumulated juices on top. Drizzle with the sesame oil.
Recipe by Genevieve Ko.