Prepare all ingredients as instructed.
Heat butter in a nonstick skillet over medium heat. Add poblano pepper and cook until softened. Add ham and cook until lightly browned.
Add spinach to the skillet and cook just until wilted.
In a bowl, whisk eggs with milk, salt, and black pepper. Pour into the skillet and cook, stirring gently, until mostly set but still soft.
Sprinkle smoked Gouda over the eggs and continue cooking gently until melted and eggs are fully cooked. Remove from heat.
Warm whole wheat wraps in a dry skillet or microwave until pliable.
Portion the egg mixture onto the wrap. Fold in the sides and roll to enclose the filling.
Brew and prepare the coffee to your liking.
Serve the wraps with kimchi, fruit, and coffee.