Bring a small pot with rice and 1 cup water to a boil over high heat. Reduce to a simmer, cover, and cook until tender, 18-20 minutes. While rice cooks, prepare ingredients.
Prepare the Ingredients
Peel, trim, and very thinly slice carrot at a very sharp angle. Cut carrot slices into matchsticks. Trim cucumber and thinly slice into rounds. Slice thin rounds from pointed half of Fresno chile. Discard seeds if you prefer less spice Stem, remove ribs, and mince other half of Fresno chile. Trim and thinly slice white portion of green onions. Slice remaining green onions on an angle. Halve lime. Juice one half and cut other half into quarters. In a mixing bowl, combine gochujang, minced Fresno (to taste), half the ginger (reserve remaining for salad) white portions of green onion, beef, and a pinch of salt and pepper.
Make the Salad
In another mixing bowl, combine carrot, cucumber, Fresno rounds (to taste), remaining ginger, 2 tsp. lime juice, 2 tsp. olive oil, ¼ tsp. salt, and a pinch of pepper.
Sear the Beef
Place a large non-stick pan over medium-high heat and 2 tsp. olive oil. Add beef to hot pan and stir occasionally, gently separating strips, until browned, 2-3 minutes. Transfer beef to a plate. Some portions may still be rare; beef will finish cooking in a later step. Reserve pan; no need to wipe clean.
Finish Beef and FInish Dish
Return pan used to cook beef to medium-high heat. Add cola and reduce to a light syrup, 5-8 minutes. Return beef and any accumulated juices to pan and coat with syrup. Cook until warmed through, 1-2 minutes. Place rice on a plate. Top with salad, then beef. Garnish with green portions of green onions and serve lime wedge on side.