Preheat oven to 350 degrees F.
In a cast iron skillet large enough to hold 1 of the pizza rounds, heat about 2 tablespoons of the olive oil. When the oil begins to smoke lightly, turn heat off and add 1 of the pizza rounds. Use a spatula to press gently on the top of the round to keep it relatively flat as it cooks. When you see it is slightly brown on the underside, season the top lightly with salt and pepper and flip the round on its second side. Season it with salt and pepper and top with the onion sausage-onion mixture and place the skillet in the center of the oven until the pizza has finished cooking, 5 to 8 minutes. Repeat with remaining dough and topping.
In a large bowl, combine the yeast and warm water. Stir to dissolve the yeast and allow the mixture to rest for 5 minutes.
Using a sieve or strainer, "sift" about half of the flour over the yeast mixture and blend until smooth with your hands. Add the salt, pepper and honey and mix to blend. Sift in the remaining flour and mix to blend.
Lightly flour a cutting board or flat surface. Turn the pizza dough onto the floured area and knead for 3 to 5 minutes. The flour should feel smooth and the ingredients fully integrated. Place the dough inside a lightly oiled large bowl. Cover with plastic wrap and let rest in a warm place, about 1 1/2 hours or until doubled in volume.
Press gently on the dough and turn it onto a floured surface. Divide the dough into 4 equal parts, rolling each quarter into a loose ball. Cover with a clean kitchen towel and allow the dough to rest for an additional 15 minutes. Flatten each ball, 1at a time, and roll into a 6-inch round. Place each round in a single layer on a lightly greased baking sheet.
In a medium skillet over high heat, heat the olive oil and cook the sausage, breaking it into small pieces as it cooks, until golden brown and crispy.
Using a slotted spoon, remove the sausage from the pan onto a paper-towel lined plate. Drop the onions into the pan and cook over medium heat until caramelized, 3 to 5 minutes. Stir in the honey.
Add the caramelized onions to the pizza fried pizza dough and top with mozzarella, sausage, basil, and a drizzle of good extra-virgin olive oil.
Tip for topping the pizza: Brushing the dough with olive oil can create a barrier that will help to prevent the topping from making the crust soggy.