Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes. Add the minced garlic and cook for an additional minute until fragrant.
Add the ground turkey to the skillet, breaking it apart with a spatula. Cook until the turkey is browned and cooked through, about 7-8 minutes. Stir in dried oregano, black pepper, and salt.
Reduce the heat to low and stir in the crumbled feta cheese and thawed spinach. Mix well until combined, then remove the skillet from heat and let cool slightly.
Take one sheet of puff pastry and roll it out on a lightly floured surface. Cut it into 4 equal squares. Place a generous spoonful of the turkey and feta mixture in the center of each square, being careful not to overfill.
Fold each pastry square into a triangle by bringing one corner to the opposite. Press the edges tightly to seal, then use a fork to crimp the edges for an extra decorative touch.
Transfer the turnovers to the prepared baking sheet. Brush the tops with the beaten egg to give them a golden finish.
Bake in the preheated oven for 15-20 minutes, or until the turnovers are golden brown and flaky.
Remove from the oven and let cool for a few minutes. Garnish with freshly chopped parsley. Serve warm, and enjoy your Crisp Garlicky Turkey Feta Turnovers!