Dissolve yeast in 3 cups warm water ina large bowl.
Add all-purpose and wholewheat flours; mix with your fingertipsuntil a shaggy dough forms. Cover bowlwith plastic wrap and let rest at roomtemperature for 20 minutes.
Sprinkle salt over dough, then addsour cream; knead until well incorporatedand dough pulls away from sides of bowland holds together in a loose, wet ball,about 5 minutes (dough will be very softand wet; lightly moisten your hands toprevent sticking if needed). Cover bowlwith plastic wrap and let dough rise at roomtemperature for 30 minutes.
Knead dough an additional 4-5 timesto deflate. Cover and chill for up to 2 days.(Dough will develop in flavor and continueto rise slowly in refrigerator.) Alternatively,let dough stand at room temperature untildoubled in volume, 3-4 hours (the warmerand more humid your kitchen is, the fasterit will rise). Chill for 1 hour before grilling tomake it easier to handle.
Build a medium-hot fire in a charcoal grill,or heat a gas grill to high. Divide dough into8 equal portions. Generously flour a worksurface. Working with 1 or 2 portions at atime (depending on how many flatbreadswill fit on your grill), roll out dough or presswith your hands into a 1/4"-thick shape. (Itdoesn't have to be perfectly round.)
Brush grill rack with oil. Grill flatbreadsuntil lightly charred on one side and nolonger sticking to grill, 2-3 minutes. Usingtongs, turn flatbreads and grill until cookedthrough, 1-2 minutes longer.