Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Place Hatch chile peppers, cut sides down, onto the prepared baking sheet.
Cook peppers under the preheated broiler until the skin has blackened and blistered, 5 to 8 minutes. Place blackened peppers into a bowl and tightly seal with plastic wrap. Allow peppers to steam as they cool, about 15 minutes. Discard skins and chop peppers.
Coat a large skillet with cooking spray over medium heat. Place shrimp onto tortilla; cover with the chiles, garlic, and mozzarella cheese. Add salt.
Fold tortilla in half and transfer to the skillet. Cook until lightly toasted with spots of brown, 3 to 5 minutes per side.