Prep the ingredients as instructed above.
Sauté the poblano and ham: In a non-stick skillet, heat olive oil or butter over medium heat. Add poblano pepper and cook for 2–3 minutes until softened. Add ham and cook for 1–2 minutes until lightly browned.
Scramble the eggs: Pour the 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 and stir gently until melted and the eggs are creamy and fully cooked, about 1 minute. Remove from heat.
Warm the wraps: Heat the whole wheat wraps 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 tightly.
Prepare the Korean Banana Milk: In a blender, combine banana, maple syrup, vanilla extract, milk, water, and ice cubes if using. Blend until smooth. Adjust sweetness or consistency as desired.
Serve the wrap with mixed fruit and Korean banana milk. Enjoy!