Rinse and drain black beans.

Stir black beans and tomatillo salsa in a saucepan over medium heat until heated through.

Remove from heat and keep warm.

Whisk eggs, green onions, salt, and pepper in a bowl.

Melt 2 tablespoons of butter in a nonstick skillet over medium heat.

Add bell pepper and mushrooms to the skillet.

Stir until mushrooms are brown, about 8 minutes.

Transfer vegetables to the bowl with the egg mixture.

Melt the remaining 1 tablespoon of butter in the same skillet over medium heat.

Add egg mixture to the skillet.

Cook without stirring until beginning to set, about 4 minutes.

Sprinkle with vegetables, Jack cheese, and 1 tablespoon of cilantro.

Cover skillet and cook until cheese melts and eggs are set, about 2 minutes.

Slide a spatula under the omelet to loosen.

Fold the omelet in half.

Turn out onto a platter.

Top the omelet with bean and salsa mixture.

Sprinkle with the remaining 2 tablespoons of cilantro.

Serve immediately.