Prepare the ingredients as instructed above.
Sauté the poblano and ham: In a non-stick skillet, heat olive oil or butter over medium heat. Add diced poblano pepper and cook for 2–3 minutes until softened. Add diced ham and cook for 1–2 minutes until lightly browned.
Scramble the eggs: Pour beaten eggs into the skillet. Stir gently until mostly set but still soft, about 2–3 minutes. Season with salt and black pepper.
Melt the cheese: Sprinkle smoked Gouda over the eggs. Stir gently until melted and eggs are fully cooked but still creamy, about 1 minute. Remove from heat.
Warm the wraps: Heat each whole wheat wrap in a dry skillet for 20 seconds per side or microwave for 10–15 seconds until pliable.
Assemble the wraps: Divide the egg mixture evenly between the two wraps. Fold in the sides and roll up tightly.
Prepare the Korean Banana Milk: In a blender, combine milk, banana, vanilla extract, and honey. Blend until smooth.
Serve the wrap with fresh fruit and Korean Banana Milk. Enjoy your breakfast!