In a large mixing bowl, mix salt into the warm water until salt is dissolved. Stir in yeast.
Stir in bread flour and semolina flour until mostly combined. Add olive oil and sourdough discard. Knead until the dough is smooth and elastic, approximately 3-4 minutes. The dough should be slightly tacky but not sticky.
Shape dough into a ball and place in a bowl. Cover with plastic wrap and allow it to rise at warm room temperature until doubled in size, approximately 1 hour.
Very lightly coat the bottoms and sides of round bowls or plastic containers with olive oil. Divide dough into 4 equal balls. Place each ball in a prepared bowl or container and cover loosely with plastic wrap or plastic container covers. Allow to rise at warm room temperature until doubled in size, approximately 1 hour.
Preheat oven (with pizza stone or pizza steel in oven) to 550℉ or to the highest temperature.
Prepare the sauce by pouring the tomatoes into a bowl. Add any spices, such as salt, Italian seasoning, oregano, or pre-made pizza spices.
Lightly coat the countertop with a drop of olive oil. Carefully pour one of the doughs onto countertop. Starting from the center of the dough, use your fingertips to press into the dough working your way out towards the perimeter of the circle. Lift the dough up, stretching it with your knuckles, so that most of the dough is very thin and the edges more doughy. Place dough onto a pizza peel (or backside of a baking sheet or a cutting board) well coated with semolina flour.
Top with mozzarella cheese, then with tomatoes. Add parmesan, if desired.
Use the peel to deliver the pizza onto the pizza stone or pizza steel. Cook for 6 minutes. Rotate the pizza 180°, and cook for an additional 2-3 minutes.
Top with a splash of olive oil (if desired) and fresh basil. Allow to cool for 1-2 minutes before slicing.