Mix the water and honey in the bowl of a stand mixer. Sprinkle the yeast on top and set aside for 10-15 minutes, until foamy.
Add two cups of the flour and gently mix until thoroughly incorporated. Cover with plastic wrap and set aside in a warm place for an hour.
Add the salt, oil, and remaining two cups of flour, and mix with a dough hook for 5-7 minutes to knead the dough. Coat the dough in oil, place it in a clean bowl, and cover it with plastic wrap. Set the dough in a warm place to rise for about an hour, or until approximately doubled in size.
Punch the dough down with floured hands and divide it into four discs. Place the discs on a lightly floured baking sheet, cover with a clean kitchen towel, and set aside to rise in a warm place for 30 minutes.
When you are ready to cook, preheat the grill to high. Flour your hands and spread each dough disc into a thin oval, allowing a little thickness around the edges. Brush olive oil onto the top of each dough oval. Carefully place pizza dough on the grill, oiled side down. Close the grill and let cook for 2-3 minutes.
Brush the tops of the dough with oil, carefully flip, and layer on your desired toppings.
Close the grill and cook for 2-3 more minutes, or until the cheese is melted. Remove from the grill, slice, and serve hot.
Notes
You can use any combination of toppings that you like. Just make sure all meats and vegetables (other than tender baby greens) are cooked beforehand, since they will not have time to cook fully on the grill. Have all your toppings ready to go right next to the grill since the cooking process moves very quickly once the dough hits the grates.If your pizza is starting to look charred on the bottom but is not as browned as you like on top, transfer it to a broiler-safe pan and finish under the broiler for 2-3 minutes, checking frequently.