Make the dough by combining flour, oil, salt, and water by hand or with a dough hook until smooth. Cover and rest for 15 minutes.
Meanwhile, prepare the filling. Melt butter in a skillet, sauté onion and garlic until fragrant, then add spinach and cook until wilted. Remove from heat and stir in mozzarella, Bulgarian cheese, and black pepper, adjusting salt to taste.
Divide the dough into 10 balls. Roll each thin, place about 2 tablespoons of filling in the center, seal the edges, and gently flatten into discs.
Cook the discs in a dry skillet over medium heat, two or three at a time, until golden on both sides, 3–4 minutes per side. Brush with melted butter and serve warm.