Prep Your Ingredients: Preheat your oven to 375°F (190°C) or your air fryer to 350°F (175°C). Line a baking sheet with parchment paper or spray your air fryer basket with oil. Unroll the crescent dough and separate it into 8 triangles or rectangles.
Assemble the Sticks: Add the mustard (if using) to each triangle, spreading a small amount thinly across the center of the dough. Lay one slice of ham over the dough, folding it to fit if needed. Place a cheese stick on top of the ham. Roll the dough over the filling, folding in the sides as you go to completely enclose the cheese. Press the edges firmly to seal and prevent cheese leakage during baking.
Brush with Butter Topping: In a small bowl, combine the melted butter, garlic powder, and parsley. Brush this mixture generously over the top of each rolled stick. Sprinkle with Parmesan cheese for a crispy, cheesy finish.
Bake or Air Fry: For oven method, place on the prepared baking sheet and bake for 12-15 minutes, or until golden brown. For air fryer method, place 2-4 sticks in the air fryer basket (depending on size) and air fry for 8-10 minutes, flipping halfway through. Let cool for 3-5 minutes before serving.