In a large bowl, combine water, yeast, honey and olive oil. Mix with a spoon, then let sit until foamy, about 10 minutes. Add the flour and salt, stirring with a spoon until the dough comes together but is still sticky. Using your hands, form the dough into a ball and work in the additional ½ cup flour, kneading it on a floured surface for a few minutes. Rub the same bowl with olive oil then place the dough inside, turning to coat. Cover with a towel and place in a warm place to rise for about 1 to 1.5 hours.

After the dough has risen, punch it down and place it back on the floured surface. Using a rolling pin or your hands, form it loosely into your desired shape. I like to get it as thin as I can here. If it’s easier, you can also cut the dough in half and do this in two separate pieces. Place the towel back over the dough to rest.

Preheat the grill to high heat for 10 to 15 minutes - you want the temperature to be around 450 to 500 degrees F. If needed, lower the temperature a little bit.

Combine the butter, garlic, herbs and a big pinch of salt in a saucepan over medium-low heat. Cook until the butter melts. Set the mixture aside.

Generously cover a pizza peel with flour and coarse grind cornmeal. This will help prevent the dough from sticking.

Moving quickly, transfer your pizza dough to the pizza peel, quickly rolling it a bit more if needed but making sure the entire bottom is floured/cornmeal very well.

Quickly and gently use a spatula or additional pizza peel to slide your pizza directly on to the grill grates. Decrease the heat directly under the pizza to low - just that single burner. Close the lid and cook until the pizza dough is bubbly and golden, anywhere from 5 to 8 minutes – but this will depend on the thickness of your crust. Just be sure to continue to check it. Flip the dough and cook for 2 to 3 minutes more. It will be finished when the edges are golden and puffed up, with a few places charred.

Remove the dough and place it on a baking sheet. Brush the melted garlic herby butter all over the dough - top and bottom. Use up all that butter!

Sprinkle it with parmesan cheese all over. Slice into breadsticks or pieces and serve!