Cook the rice according to package directions. While it cooks, whisk the soy sauce, brown sugar, gochujang, and sesame oil in a small bowl. Thinly slice the cucumber and toss it with the rice vinegar and a pinch of sugar. Set it aside.

Heat a drizzle of vegetable oil in a large skillet over medium-high heat. Crumble in the ground beef and cook, breaking it up, until browned and no pink remains, about 5 minutes. Drain excess fat if needed. Stir in the garlic and ginger and cook 1 minute more.

Pour the sauce over the beef. Bring it to a simmer, then cook for 2 to 3 minutes, stirring, until the sauce thickens and coats the meat.

Divide the rice among bowls. Top with the beef, pickled cucumber, carrot ribbons (use a peeler), scallions, and sesame seeds. Serve right away.