Prepare the ingredients as instructed.
Heat butter in a non-stick skillet over medium heat. Add diced poblano pepper and cook for 2–3 minutes until softened. Add diced ham and cook 1–2 minutes until lightly browned.
Pour beaten eggs into the skillet. Stir gently until mostly set but still soft, about 2–3 minutes. Season with salt and black pepper.
Sprinkle smoked Gouda cheese over the eggs. Stir gently until melted and the eggs are creamy and fully cooked, about 1 minute. Remove from heat.
Warm the whole wheat wraps in a dry skillet for 20 seconds per side, or microwave for 10–15 seconds until pliable.
Portion the egg mixture onto each wrap. Fold in the sides and roll tightly to enclose the filling. Cut in half.
Brew and prepare the coffee to your liking.
Serve wraps with kimchi, fruit, and coffee.