Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper or foil.
Separate the prosciutto slices gently and lay them flat on a clean surface.
Drain mozzarella balls and cut in half if large for easier wrapping.
Place one mozzarella ball at the center of each prosciutto slice and wrap fully.
Heat olive oil in a skillet over medium heat, then add oregano, garlic powder, and black pepper.
Stir the seasonings in olive oil for 30 seconds until fragrant, then remove from heat.
Brush the seasoned olive oil over each wrapped mozzarella bite.
Arrange the bites on the prepared baking sheet, spaced slightly apart.
Bake for 10 to 12 minutes until prosciutto is crispy and golden.
Remove from oven and let cool for a few minutes before serving.
Optionally, sprinkle fresh basil on top before serving.