In a medium bowl, combine the spinach, cheeses and flour. Set aside.
Preheat oven to 400°F.
In a large bowl, combine the water, yeast and sugar and let proof for 10 minutes.
Combine the oil with the salt and add to the yeast mixture.
Using a standing mixer with a dough hook or by hand, start incorporating the flour, one cup at a time. Dough should come together in 3-5 minutes and be just a bit sticky.
Pour vegetable oil onto a baking sheet until it reaches halfway up the sides.
Roll the dough into golf-ball-sized pieces, then place on the baking sheet and leave covered with towel for an hour.
Using a small rolling pin, roll out the dough as thinly as possible, then sprinkle with Parmesan cheese.
Add a little of the filling and roll the dough like a jelly roll.
Coil the roll into a snail and place on a baking sheet. Repeat to make all the bulemas.
Brush with egg wash and sprinkle with grated cheese.
Place in the oven and bake until the bulemas are a golden brown, about 15 minutes.