Preheat oven to 400F. Line 2 baking sheets with parchment paper and set aside.
Start by heating the oil in a skillet. Add the diced onion and cook for 5-7 minutes until they are translucent and lightly golden around the edges. Add the garlic and cook an additional minute.
Squeeze as much liquid as you can out of the spinach and add it to the pan. Cook for 2-3 minutes, stirring often. Set the spinach mixture aside to cool.
Once it's cooled, add the cheeses and mix well.
Lightly roll out the puff pastry and spread half of the spinach and cheese mixture over it, leaving a small border at the top edge. Next, roll it into a tight spiral log and seal the edge by pressing it gently.
Repeat this step with the second sheet of puff pastry.
Roll the logs in plastic wrap and freeze for 20 minutes. Use a serrated knife to slice into pinwheels and place on to the prepared baking sheets. Brush with egg wash.
Bake for 20-22 minutes, until puffed and golden.
