Combine the warm water, salt, oil, honey, and lemon juice in the bowl of a stand mixer.
Next add half of the flour. Mix until well combined.
Allow the dough to rest in the mixer for 10 minutes.
Add the yeast and the rest of the flour, ½ cup at a time and watch how the dough reacts. You don’t want to add too much flour. Add just enough to where a soft dough forms and the dough begins to pull away from the sides of the bowl.
Knead the dough until it reaches windowpane.
Cover the dough and allow to rise until doubled in size, about 1 hour.
Spray a large piece of parchment paper and put it on a large pan. Set aside.
Turn the dough out onto a lightly oiled surface and cut into 4 equal pieces.
Roll one of the pieces out into a 10 inch circle and place it onto the parchment paper. Brush with the egg wash.
Spread out 2 tablespoons of the pesto over it and sprinkle with ¼ cup of the parmesan cheese, leaving about ¼ inch headspace from the edges.
Do the same with the 2nd and 3rd pieces of dough. Place each layer on top of the preceding layer, brush with the egg wash, spread the pesto, and sprinkle with the parmesan.
Roll out the last piece of dough in a 10 inch circle and place on top of everything. Push down on the edges, to make sure the filling doesn't spill out.
Place a cup or dish that is 3 inches in diameter in the center of the circle. Press lightly to make an indention. Do not make a cut with it.
Use a knife to cut 16 equal strips all the way around the circle, stopping at the indentions that you made with the cup.
Take two adjacent strips, twist them two times and connect them at the ends, making a point. Continue to do this all the way around the circle, until you have 8 star tips.
Cover and let rise in a warm spot for about 30-40 minutes, until puffy.
Preheat the oven to 400 degrees F.
Brush with egg wash and bake for 17-20 minutes, until golden brown.