Heat oil in a medium skillet over medium heat. Add bell pepper, scallion whites, and cumin; cook, stirring often, until softened, 1 to 2 minutes.
Add beans, cooked barley, broth, and salt. Cook until most of the liquid is absorbed, 3 to 5 minutes.
Stir in scallion greens and hot sauce. Divide between 2 bowls.
Place ½ cup water and ½ tsp. vinegar in a microwave-safe small bowl. Carefully crack 1 egg into the water so it is completely submerged.
Cover with a microwave-safe plate and microwave on High until the egg white is firm and the yolk is still somewhat runny, about 1 minute. (If necessary, continue to microwave, checking every 10 seconds.)
Remove the egg with a slotted spoon, pat dry and place atop the bean mixture in 1 bowl. Repeat with the remaining ½ cup water, ½ tsp. vinegar, and egg.
Top each bowl with 1 Tbsp. cheese and ¼ avocado. Sprinkle with cilantro, if desired.
