1. In 2-quart saucepan, place potato chunks and enough water to cover; heat to boiling over high heat. Reduce heat to low; cover and simmer 15 minutes or until potato chunks are fork-tender. Drain potatoes. Return potatoes to saucepan; heat over medium heat, shaking pan constantly, until excess liquid evaporates, about 30 seconds. With potato masher, mash potatoes until smooth. Set aside until cool, about 20 minutes.
2. In small bowl, stir honey and yeast into 1/4 cup warm water (105 to 115 degrees F.); let stand until yeast mixture foams, about 5 minutes.
3. In large bowl, with wooden spoon, stir cooled mashed potatoes, yeast mixture, yogurt, and salt until combined. Stir in whole wheat flour and about 2 1/4 cups all-purpose flour or enough to make a soft dough. With floured hand, mix dough in bowl and shape into a ball. Cover bowl with plastic wrap and refrigerate dough overnight.
4. When ready to bake, turn dough onto well-floured surface and knead until smooth and elastic, about 10 minutes, working in more all-purpose flour (about 1 cup) while kneading (dough will be sticky). Cut dough into 16 equal pieces; with floured hands, shape each into a ball and place in 15 1/2" by 10 1/2" jelly-roll pan. Cover pan and let dough rise in warm place (80 to 85 degrees F.) until doubled, about 40 minutes.
5. Preheat oven to 450 degrees F. Place oven rack in center of oven. On floured surface, with floured rolling pin, roll 1 piece of dough into a 6-inch round, being careful to keep thickness of dough even. (If dough is too thick or too thin, pitas will not rise uniformly when baked.) Repeat with 3 more pieces of dough. With pastry brush, remove excess flour from pitas.
6. Heat large cookie sheet in oven 5 to 7 minutes. Place 4 pita rounds on preheated cookie sheet; bake 5 minutes or until golden and puffed (some pitas will puff more than others). Cool on wire rack. Repeat with remaining dough.