Makes 8 5-inch rounds
Lightly oil 2 baking sheets and large bowl; sprinkle sheets with half of sesame seeds. Combine water, yeast and sugar and let stand 5 to 10 minutes.
Steel knife: Place cake flour, 1 1/2 cups unbleached flour, salt and yeast mixture in work bowl. Blend well using on/off turns. Add remaining flour by tablespoonfuls (it may not be necessary to use all of it), incorporating after each addition with 3 to 4 on/off turns. Dough should be sticky but not wet; check consistency by touching. When dough is proper consistency, add oil and let machine run about 40 seconds (or no more than 60 seconds) to knead. (Dough will appear smooth. ) Place in prepared bowl, rotating so all surfaces are coated with oil. Cover with damp towel, set in a warm place, and allow to double in bulk, about 1 hour. When dough has doubled, punch down. Allow to rest 30 minutes in bowl on counter top.
Place racks on upper shelves and preheat oven to 500 F. Lightly flour board and place dough on flour. Cut in half, then cut each half into quarters to make 8 equal pieces. Flatten each piece with palm of hand, then roll into a circle no more than 5 inches in diameter. Place on prepared sheets and sprinkle with remaining 1 Tbs sesame seeds, lightly pressing seeds into both sides of dough. Bake about 8 to 10 minutes, only until delicately browned. Do not overbake; these are better slightly doughy. (It may be necessary to reverse the sheets after 6 minutes to brown the pita evenly. ) Allow to cool slightly. Cut pita in half with scissors and separate opening. Wrap in foil to maintain freshness if not served immediately.