Crumble the yeast into a bowl. Add water, oil, salt, sugar, and most of the flour. Knead the dough until smooth - about 8-10 min. Let the dough rise in a damp cloth for about 30 minutes. Heat the oven to 225 degrees.
Sprinkle a little flour on the table and divide the dough into 4 pieces. Roll each piece into about ½ cm thickness. Place the bottoms on baking sheets with baking paper. Crumble the feta cheese coarsely and spread on the bottoms. Sprinkle also the grated yellow cheese. Bake in the middle of the oven for 12-15 minutes.
Cut the tomatoes into wedges and remove the seeds. Cut the tomatoes into small cu-bes. Remove the skin of the red onion and garlic clove and chop both finely. Remove the seeds from the chili and chop it. Mix all the ingredients for the tomato mixture.
Brush the edges of the finished pizza with olive oil. Add the tomato mixture on the pizza and sprinkle with olives and basil.