Preheat your oven to 425°. If you have a pizza stone, place it in the oven as it heats. If not, line one upside-down baking pan with parchment paper and set it aside.
Divide the pizza dough into 4 equal portions, and roll each into a ball. Set the dough aside, covered loosely with a wet towel.
In a medium saucepan, combine 2 tablespoons of olive oil with the onion.
Sauté, stirring frequently, over medium heat, until the onion is translucent (about 5 minutes). Add the minced garlic and the pancetta. Sauté, stirring frequently, until the garlic is fragrant and the pancetta is cooked (about 4 minutes). Remove the onion garlic and pancetta mixture to a separate large bowl.
Add the fresh spinach to the saucepan, and cook over high heat, stirring frequently, until wilted (about a minute), and add to the large bowl with the other ingredients. If using frozen spinach, don’t cook and just toss directly into the large bowl.
Mix to combine, adding salt and pepper to taste. Set the bowl aside to cool.
Take the first ball of pizza dough, and roll between two pieces of parchment paper into an approximately 6–8-inch round, about ⅛ inch thick (thickness of a nickel). If the edges are very rough, tuck them toward the center of the round, and then roll them smooth. Repeat with the remaining balls of dough. Place each dough round on the overturned baking pans or warmed pizza stone.
To the large bowl, add the ricotta, parmesan, gruyere and eggs, and mix to combine well. Fold in the basil and oregano.
Divide the filling between the 4 rounds of pizza dough, placing the filling on one half of the dough, leaving a 1-inch border of bare dough. Fold the opposite end of the dough over the filling, and pinch together the edges well until there is a good seal. Brush the tops and seams with the melted unsalted butter and olive oil. Place the overturned baking pan or pizza stone in the center of the preheated oven and bake for about 15 minutes or until nicely golden brown and crisp.
Serve right away.