Pizza Dough and Margherita Pizza

I have made homemade pizza dough many times and am always very disappointed.  It comes out hard and tough.  Edible, but barely.  I follow directions pretty well, so I guess they were just bad recipes.  I finally found a great one!!  It was fabulous!  YAY!
Okay, so enough rejoicing and on to the recipe!  I apologize for the shape of my pizza's.  I tried the method in their directions telling me to make the pizza and transfer it to the hot pizza stone (not possible), and will tell you how to do it right.  The key is, make this around 2 pm, if possible or day before and chill after first rise. 

PIZZA DOUGH 

INGREDIENTS:

• 1/2 cup very warm water (110 degrees, I used thermometer)
• 1 envelope (2 1/2 tsp.) active yeast
• 1 1/4 cups room temp. water
• 2 TBSP extra-virgin olive oil
• 4 cups bread flour (I used almost 5 to get it to hold together)
• 1 1/2 tsp salt
• 1 1/2 tsp sugar
• olive oil for greasing bowl

DIRECTIONS:

Measure  the 1/2 cup warm water in glass measuring cup.  Sprinkle in yeast and let stand for 5 minutes until it swells.  Stir with wooden spoon to ensure it is all incorporated.  Add the reamins water and olive oil and stir.

Place flour, salt and sugar into bowl of stand mixer fitted with paddle attachment.  Combine dry ingredients.  Slowly add wet ingredients and mix until a cohesive mass forms.  Swith out paddle with hook attachment and turn on low for about 5 minutes to knead, adding flour if necessary so it is not too soft or sticky.  (NOTE:  Will still be very soft and somewhat sticky, just want it somewhat workable, for me that meant about another 3/4 cup flour than the 4 called for).  Put into oiled bowl and turn so top is also oiled and cover with plastic wrap.  Let rise for 2 or more hours(I let mine go 2.5 hrs.).
Preheat oven to 500 degrees with pizza stone inside for 30 minutes.  Press to deflate and divide into 2 equal pieces.  (Here is where you chill if desired)Put them both on floured surface and cover with a damp towel.  Leave for 10-30 minutes.  (can use pizza peel here or parchment on cookie sheet, but I opted to do it this way)  Remove stone from oven and sprinkle with cornmeal.  Pick up a dough.  Should spread really easy into circle.  Get into shape as much as possible because once on the stone it will somewhat seal the shape.  Place on stone.  Top as desired. Cook until cheese is golden and crust begins to color, 8-12 minutes.

For a variation mix in some Italian herbs to the dough.
For Margherita Pizza:

• 2 garlic cloves
• 1.5 TBSP EV olive oil
• some oregano 
• mozzarella
• fresh sliced tomatoes 
• thinly sliced basil
• salt and pepper

Mix olive oil, garlic and some oregano and spread over dough with fingers.  Top with cheese, tomatoes and basil and salt and pepper.