Fill a sink with cold water. Place a cutting board nearby. Stack 4 collard green leaves on top of each other. Remove the stems with a sharp knife, and trim 2 inches from the bottoms of each stem. Cut the stems into 1⁄8-inch pieces. Cut the leaves into 2-inch squares.  Repeat with remaining leaves. Rinse the leaves and stems in cold water. Drain.

Heat 1 tablespoon of the vegetable oil in a medium sauté pan or skillet over medium. Break the egg into the pan, and cook 4 minutes, gently shaking the pan occasionally to ensure the egg does not stick. Sprinkle with the salt and pepper. Turn the egg, and cook 2 more minutes. Transfer to a plate, and keep warm.

Heat the remaining 1 tablespoon vegetable oil in the sauté pan over medium. Add the shallot, garlic, and ginger. Cook, stirring occasionally, until shallot is translucent. Add the collard leaves and stems to the pan; cook, stirring constantly, 1 minute. Stir in the vinegar. Stir in the soy sauce and mirin. Stir in the rice, and cover. Simmer until the rice is heated through, about 2 minutes. Uncover and drizzle with sesame oil. Remove from heat, and let stand 2 minutes.

Transfer the fried rice to a serving bowl. Cut the fried egg into 1⁄8-inch-thick strips. Top the rice evenly with the egg strips. Garnish with the scallions, jalapeño slices, sesame seeds, lime wedges, and red pepper flakes, if desired.