Combine warm water, sugar and yeast in a medium bowl. Set aside for 10 minutes, allowing the mixture to bloom until frothy and foamy.
Stir together the flour and salt in a large bowl. Add the water, sugar and yeast mixture, as well as the melted butter. Mix with a wooden spoon until the dough comes together.
Transfer the dough to a floured surface and knead until smooth.
Using melted butter, grease a large bowl. Add the dough to the bowl and cover it loosely with plastic wrap and a kitchen towel. Set in a warm spot and allow the dough to double in size. This will take about 1 hour.
While in the bowl, punch the dough down and then divide evenly into 3 pieces – roughly about 209 grams each – and form each into a ball.
Place the dough balls on a lightly floured platter or baking sheet. Cover platter or sheet loosely, allowing dough to rest once more until doubled in size. This will also take about 1 hour.
Preheat an outdoor grill or stovetop grill pan over medium heat.
On lightly floured platter or sheet, roll out each dough ball to about a 9-inch circle. Brush with melted butter and place the buttered side down onto the hot grill.
Cook for about 2 minutes on the first side, or until the dough slightly charred and golden. Flip over and cook for another 2 minutes. Take the pizza off grill, transferring to a platter. Repeat for the rest of the pizza dough. You may be able to add all your pizza doughs to the grill at the same time, depending on your grill size.
For each grilled pizza, spread on peanut butter. Then, sprinkle with chocolate, marshmallows and graham cracker pieces. Return the pizzas to the grill, cover and cook for about 2 to 3 minutes, until the chocolate has melted, and the marshmallows have softened.
Remove the pizzas from the grill, slice and serve immediately. Enjoy your decadent grilled dessert pizza!