Place eggs, vanilla, sugar, flour and milk in blender. Blend for 1 minute. Scrape the sides to get all ingredients incorporated. Blend for 1-2 more minutes or until well blended and frothy. Set aside.
Add butter and coconut oil to 10" nonstick skillet and place in oven. Watch closely to make sure mixture melts but doesn't burn. As soon as the mixture melts, using an oven mitt, swirl the mixture to coat.
Pour mixture from the blender over the butter mixture in skillet. Return skillet to oven and bake for 20 minutes. Reduce heat to 350°F, and bake for 5 more minutes.
Remove from oven and drizzle with half the Nutella, sprinkle with coconut, then drizzle with remaining Nutella. Cut into 4 wedges with a spatula and serve immediately.
The milk needs to be heated a bit to bring up the temperature of the batter so it's not refrigerator cold when it goes into the oven to make a more stable puff.
The Nutella needs to be briefly heated to thin it out a bit and make it more drizzly.
Work quickly once the Dutch baby comes out of the oven. I have a trivet ready to go to place the hot skillet on, I heat my Nutella during the last 3 minutes of the baking time so it can be placed within reach of the skillet on the trivet, and I have the coconut ready to go and placed right next to everything as well.