In the bowl of your standing mixer, combine the yeast, sugar, and water. Let the yeast activate or “bloom” for about 5-10 mins until it is bubbly.
With the hook attachment on, add 1 cup of flour and mix. Gradually add the second cup of flour until a soft dough forms. Go slowly. You might not need the whole cup.
Add the olive oil to the bowl and swirl it around so that it covers the dough entirely. Place a damp towel on top of the bowl and let the dough rest in a dry place for about 40 mins. In a small bowl, mix the tomato puree, tomato paste, garlic, Italian seasoning, fresh basil, salt, and pepper. This will be your sauce. Preheat the oven to 450 F.
When the 40 mins are up, take the dough out of the bowl and, using your hands, press it onto the pizza baking sheet, leaving a border all around.
Spread the sauce over the pizza dough evenly
Sprinkle both kinds of cheese on top of the sauce evenly and bake for about 20-30 minutes or until the cheese is melted and bubbly.