Stir warm water and sugar in small bowl until sugar is dissolved. Sprinkle yeast over top.Let stand 10 minutes. Stir until yeast is dissolved.
Combine first amount of flour and salt in large bowl. Make a well in the center. Add first amount of olive oil and yeast mixture to well. Mix until combined.
Work in enough of second amount of flour until dough pulls away from sides of bowl and is still slightly sticky. Turn out onto lightly floured surface. Knead for 3-5 minutes, adding flour if necessary to prevent sticking,until smooth. Place in greased extra large bowl, turning once to grease top. Cover with greased wax paper and tea towel. Let stand in oven with light on and door closed for about 1 1/2 hours until tripled in bulk. Punch down dough.
Turn out onto lightly floured surface. Knead for 1 minute. Shape into a ball. Flatten slightly. Sprinkle with first amount of Parmesan cheese, oregano and garlic. Press down lightly. Fold dough in half to enclose filling. Knead for about 3 minutes until evenly combined. Roll out or press into greased 12 inch pizza pan. Cover with greased wax paper and tea towel. Let stand in oven with light on and door closed for about 45 minutes until doubled in size. Poke indentations over surface of dough with fingers or wooden spoon handle, about 1/4 inch deep and 1 1/2 inch apart.
Drizzle second amount of olive oil evenly over over dough. Oil will pool in indentations. Sprinkle with second amount of Parmesan cheese. Bake in 425°F oven (400°F in convection) for about 20 minutes until golden brown. Let stand in pan for 5 minutes before removing to wire rack to cool. Cut into wedges.