Freeze the Nutella. Line a small plate with parchment.
Dollop 18–20 teaspoon-sized mounds of Nutella, then freeze for 20–30 minutes until firm. This keeps the center from melting out while frying.
Make the batter. In a bowl, whisk flour, sugar, baking powder, and salt. In another bowl, whisk egg, milk, and vanilla.
Combine wet and dry until smooth and thick, like pancake batter. If too thick, add 1–2 tablespoons of milk.
Heat the oil. Pour 2–3 inches of oil into a heavy pot. Heat to 350–360°F (175–182°C).
Keep a thermometer handy to maintain temperature.
Assemble the Oreos. Place a frozen Nutella disc on top of each Oreo. Gently press so it sticks. If you prefer, sandwich Nutella between two Oreos and press lightly—just note these will be larger and need a few extra seconds to fry.
Batter and fry. Working in small batches, dip each Oreo into the batter, turning to coat fully.
Let excess drip off. Carefully lower into hot oil. Fry 60–90 seconds per side until deep golden.
Avoid crowding the pot.
Drain and dust. Transfer to a paper towel–lined tray to drain. While warm, dust generously with powdered sugar. Add optional drizzles or toppings immediately so they stick.
Serve warm. These are best hot and fresh, when the Nutella is molten and the shell is crisp.