Step 1: Prepare the shrimp. In a medium skillet, melt 1 tbsp butter over medium heat. Add the chopped shrimp and minced garlic. Sauté for 2-3 minutes, or until the shrimp are pink and cooked through. Remove from heat and let cool slightly.
Step 2: Make the creamy filling. In a medium bowl, combine the softened cream cheese, mayonnaise, and finely chopped chives. Mix until smooth.
Step 3: Combine ingredients. Add the cooked shrimp and shredded mozzarella (or Gruyère) to the cream cheese mixture. Season with salt and pepper to taste. Mix gently until all ingredients are well combined.
Step 4: Preheat oven and prep croissants. Preheat your oven to 350°F (175°C). Carefully slice each croissant horizontally, almost all the way through, creating a pocket. Do not cut completely in half.
Step 5: Stuff and egg wash. Spoon a generous amount of the creamy shrimp mixture into each croissant. If desired, whisk the egg with 1 tsp of water to create an egg wash, and brush lightly over the top of each stuffed croissant for a golden finish.
Step 6: Bake. Place the stuffed croissants on a baking sheet. Bake for 10-15 minutes, or until the croissants are golden brown and the filling is warm and bubbly.
Step 7: Garnish and serve. Remove from the oven, garnish with extra fresh chives or parsley, and serve warm immediately.