Add the warm water into a small mixing bowl or a standard 2 cup measure, sprinkle the yeast over the warm water and let stand until the yeast softens, 3 to 5 minutes. Mix slightly to dissolve yeast and allow it to proof for another 15 minutes in a warm spot in the kitchen. Add the room temperature water and 1 tablespoon of the olive oil to the yeast mixture and stir to combine. Measure the flour and the salt into the bowl of a stand mixer. Combine on very low speed with the paddle attachment. Slowly add the liquid ingredients to the dry, and increase the speed of the mixer slightly to incorporate the mass. Stop the mixer and replace the paddle with a dough hook if you have one. Knead until the dough becomes smooth and begins to pull away from the sides of the bowl, about 4 minutes. Place the dough on a floured board and knead the dough by hand for another 1 to 2 minutes. Add flour to dust as needed to prevent sticking. Shape the dough into a ball and place in a very lightly oiled bowl and cover with a clean towel, let stand until dough doubles in size, about 1 hour.
When the dough has doubled in bulk, divide it into 6 equal pieces (about 6 ounces each). Set the pieces of dough being used on a sheet pan and cover with a clean towel or plastic wrap. (Dough not being used can be placed in the refrigerator or frozen until ready to use.) With a rolling pin on a lightly floured surface, roll each piece of dough as evenly as possible into a 10-inch circle, dusting lightly with flour, as necessary.
Cover with toppings and bake until golden brown, about 10 minutes.