Measure the water in a glass-measuring cup.
Stir in the yeast and sugar. Let rest for in a warm place.
After 5 to 10 minutes, the mixture should be foamy, indicating the yeast is "alive".
If it does not foam, discard it and start again.
Pour the water/yeast mixture in the bowl of a food processor. Add 1 cup of the flour as well as the salt and 1/4 cup of olive oil. Pulse several times to blend. Add the remaining flour, Italian herbs, and hot pepper flakes.
Process the dough until it's smooth and elastic and pulls away from the sides of the bowl, adding small amounts of flour or water through the feed tube if the dough is respectively too wet or too dry.
Let the dough rise in the covered food processor bowl in a warm place until doubled in bulk, about 1 hour.
Remove the dough from the food processor (it will deflate) and turn onto a lightly floured surface.
Oil two 8- to 9-inch round cake pans generously with olive oil. (Just pour a couple of glugs in and tilt the pan to spread the oil.) Divide the dough into two equal pieces, shape into disks, and put one in each prepared cake pan.
Oil the top of each disk with olive oil and dimple the dough with your fingertips. Sprinkle lightly with coarse salt, and if desired, additional dried Italian herbs.
Cover the focaccia dough with plastic wrap and let the dough rise in a warm place, about 45 minutes to an hour.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 400F and preheat, lid closed, for 10 to 15 minutes.
Put the pans with the focaccia dough directly on the grill grate. Bake until the focaccia breads are light golden in color and baked through, 35 to 40 minutes, rotating the pans halfway through the baking time.
Let cool slightly before removing from the pans. Cut into wedges for serving.