Place a large 10-12 inch cast iron skillet in the middle of the oven and preheat to 450°F.
Zest the lemon in a bowl and add the sugar. Using a fork mix the lemon zest and sugar together until fully combined, using the back of the fork to press the zest into the sugar to release the oils. Set aside.
Using an electric stand mixer, whisk together the room temperature eggs, half and half (or whole milk), flour, salt, vanilla, and 4 tablespoons melted butter. Beat until the batter is smooth, about 2 minutes. Make sure there are no large clumps of flour at the bottom of the bowl. The batter will be thin.
Once the oven has preheated with the skillet, carefully add the remaining 4 tablespoons of butter, swirling to coat the bottom of the pan. It will bubble and brown. Immediately add the batter and return skillet to oven. Top with 3 tablespoons of the lemon sugar and bake until puffed and golden-brown, 13-15 minutes. Do not open the oven for the first 10 minutes of baking, or you may deflate the dutch baby.
Serve with fresh sliced strawberries, chamomile cream, remaining lemon sugar, or a light dusting of powdered sugar or pure maple syrup! ENJOY!