In the bowl of a standing mixer, combine water, yeast, and sugar. Let rest 10 to 15 minutes until foamy.
Add the all-purpose flour, olive oil, and salt to the mixer and beat on low until the dough pulls away from and cleans the sides of the bowl. The dough should feel tacky but not sticky.
Place in a lightly greased container and cover until doubled in size, about 1 hour to 1 1/2 hours.
Turn the dough out onto a lightly greased surface. Divide the dough and shape into two rounds.
Place the dough on a lightly greased sheet. Cover and refrigerate for 30 minutes.
While the dough chills, place a pizza stone inside the Traeger and preheat at 450° Fahrenheit (232° Celsius).
Remove dough from the refrigerator. Lightly sprinkle a high-heat parchment paper with cornmeal. Roll out and shape the dough on the parchment paper.
Add sauce and toppings according to personal preference.
When ready, use a pizza peel to transfer the dough to the pizza stone. Bake at 450° for 15 to 20 minutes.
While the first pizza cooks, shape and prepare the second round of dough.
Use a pizza peel to remove the pizza onto a pizza pan. Transfer the second pizza into the Traeger and bake for the same amount of time.