Combine the dry yeast, sugar and 4 tbsp water. Leave in a warm place for about 15 minutes to bubble. Mix the flour with the salt, place it in a large bowl, make a hole in the middle. Pour in the olive oil, yeast and remaining water into it and knead the dough. Then put the dough on a floured surface and knead for 4-5 minutes.
Return it back to the bowl, cover with a cloth and leave to rise (to approximately double in volume) in a hot area. Knead the dough for about another 2 minutes, stretch it with your hands and spread it in a baking dish (or a specialized pizza pan) evenly. With your fingers, stretch it to the ends to make it even.
The dough must not be thicker than 1/4″ (6 mm), because it will swell during cooking. Put in the chopped canned tomatoes, garlic, parsley, olive oil and salt in a large pot. Boil about 20 minutes until the sauce thickens. Add the tomato paste and let it cool slightly.
Smear the pizza dough with tomato sauce, arrange the mozzarella pieces on top, sprinkle with grated parmesan cheese and bake in a preheated oven at 392°F (200 °C) for about 20 minutes. Serve hot.