In a bowl, combine the dry yeast and sugar with the lukewarm water and olive oil. Whisk, briefly, to dissolve everything and let it proof for 5-10 minutes. You will know when to stop when the liquid looks all frothy as if it were covered in sea foam.
In a separate bowl -preferably the working bowl of your stand mixer- (this is a stand-mixer recipe; if you want to do it by hand, see below) combine the two types of flour, the salt, and the garlic powder. Add the dried basil by rubbing the leaves together between your fingertips to reduce it to a powder.
Mix the dry ingredients together until everything is equally distributed.
Pour the wet ingredients into the dry and stir to combine.
If in a stand-mixer, use your dough-hook. Beat the combined dough at the highest speed you can for 5 - 6 minutes. ALTERNATIVE: If doing this by hand, dust your counter top with a little bit of flour to prevent sticking and start folding the mixed dough over with your hands, and pressing it flat. Turn 45-degrees, fold, press, and repeat. Knead like this with your full-strength for about 7 minutes.
Lightly spread some olive oil around the sides of a clean, large bowl as well as on the surface of the rounded dough ball you have made. Place the dough into this bowl.
Cover the top of the bowl with a clean light-weight towel, place it in a warm part of the room, and let it rise for 1-1/2 to 2 hours.
When it has risen, divide the dough into two balls and roll it out to an oval about the size of your pizza stone.
Once you have your round, flat dough ready, put it on a cutting board or other, flat surface with a small dusting of yellow corn meal beneath it. This is an old trick that I learned while making pizzas, years ago, in a restaurant. The corn meal will allow the dough to slide around easily and will help when you go to slide it into your heated oven and onto the pizza stone.
Add your sauce and desired pizza toppings (try to keep it to 3 or less, including cheese, for the best results) and place on a hot stone or pan that is in an already-hot 450-degree (Fahrenheit) oven. NOTE: A good pattern I have learned from years of making pizza is: first layer - sauce, second layer - half of your cheese, third layer - your non-cheese toppings, and fourth layer - the remainder of your cheese.
Cook for 13 - 16 minutes or until any cheese turns brown in little spots.
Let your pizza rest for 10 minutes before cutting.