In a medium bowl combine shredded mozzarella, grated Parmesan, Italian seasoning, garlic powder, salt, and black pepper. Toss until evenly distributed.

Make egg wash

In a small bowl beat the egg with 1 teaspoon water until combined. Set aside.

Arrange wrappers

Lay out 6 wonton wrappers at a time on a clean work surface, keeping the remaining wrappers covered with a damp towel to prevent drying.

Assemble Goat Sticks

Portion filling

Place about 2 tablespoons of the cheese mixture in the center of each wonton wrapper. (If you prefer longer sticks, use 1 tablespoon per wrapper and roll two wrappers per stick as described next.)

Roll and seal

Brush the edges of each wrapper lightly with the egg wash. Fold one corner of the square over the filling to form a triangle, then roll tightly away from the folded point to create a stick about 3–4 inches long. Press edges to seal; if needed, use a little egg wash to secure seams. Repeat to make 6 sticks (use 6 wrappers if filling is generous, or double-wrap for longer/stronger sticks).

Prep for baking

Place the rolled sticks seam-side down on a parchment-lined baking sheet. Lightly brush each stick with olive oil and sprinkle a pinch of extra Italian seasoning or Parmesan on top if desired.

Cooking

Bake

Preheat oven to 400°F (200°C). Bake the sticks on the middle rack for 10–12 minutes or until wrappers are golden brown and cheese is melted. Rotate the pan once halfway through baking for even browning.

(Optional) Air-fryer method

Preheat air fryer to 375°F (190°C). Place sticks in a single layer (do not overcrowd) and air-fry for 6–9 minutes, checking after 6 minutes, until golden and cheese is melted.

Serve

Warm the marinara sauce in a small saucepan over low heat or microwave until heated through (about 1–2 minutes). Spoon the marinara into a small bowl for dipping.

Transfer baked Goat Sticks to a serving plate. Garnish with fresh basil leaves and a light sprinkle of red pepper flakes if using. Serve immediately with warm marinara for dipping.