In a large mixing bowl, place warm water, yeast, olive oil, honey, garlic and chopped basil; allow to sit for ten minutes to activate the yeast. (Bloom)
Add the flour and salt to the yeast mixture and mix to incorporate.
You may use a fancy mixer or do the whole thing by hand in a large bowl. If using a mixer, mix until the dough cleans the sides of the bowl, about 5 minutes. After the dough is mixed, pour out into a lightly floured surface and knead for about five - ten minutes.
Place into a lightly oiled bowl and roll the dough around to coat with oil. Cover with plastic wrap or a damp towel. Let sit in a warm place until it has doubled in size, 30-60 minutes.
Punch dough down to remove the air. Split the dough in half and form it into two equal rounds. Place both on a greased pie pan. Rub the top of each round with olive oil and sprinkle with the chopped tomatoes, black olives, red onions, and parmesan cheese.
Allow the dough to proof a second time. When the dough has risen to twice its original size, bake it in a 350 degree oven until golden brown and cooked evenly through.
*Do Not add salt directly to the yeast or it will KILL the yeast.
*It's best to mix the salt into the flour BEFORE adding it to the yeast water