Dissolve yeast in warm water in a large bowl; let stand 5 minutes.
Lightly spoon flours into dry measuring cups; level with a knife.
Place cottage cheese in a food processor; process 20 seconds or until smooth. Add brown sugar, butter, and eggs. Process just until blended. Stir cottage cheese mixture, whole wheat flour, and salt into yeast mixture. Stir in enough all-purpose flour to form a soft dough. Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, one tablespoon at a time, to prevent dough from sticking to hands. (Dough will feel sticky.)
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Press 2 fingers into dough. If indentation remains, the dough has risen enough.)
Punch dough down; cover and let rest 5 minutes. Divide in thirds. Working with one portion at a time (cover remaining dough to keep from drying), shape each portion into 12 balls. Place balls in muffin cups coated with cooking spray. Repeat procedure with remaining two-thirds of dough.
Cover and let rise 30 minutes or until doubled in size.
Preheat oven to 375°.
Bake at 375° for 12 minutes or until golden. Immediately remove rolls from pans.
NOTE: Dough balls may be frozen for 2 weeks. To prepare, place frozen balls in muffin cups. Let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. Bake as directed.