Dissolve sugar and yeast in warm water in a large bowl; let stand 5 minutes. Lightly spoon flours into dry measuring cups; level with a knife. Add flours, milk, and next 3 ingredients (milk through oil); beat with a mixer at medium speed until smooth.
Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes).
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 two fingers into dough. If indentation remains, the dough has risen enough.)
Punch dough down. Cover and let rest 5 minutes. Turn dough out onto a lightly floured surface. Arrange olives over dough; knead gently 4 to 5 times or until olives are incorporated into dough. Cover and let rest 10 minutes.
Preheat oven to 375°.
Punch dough down. Divide dough into 16 equal portions. Working with 1 portion at a time (cover remaining dough to keep from drying), roll each portion into a 2-inch ball. Repeat procedure with remaining dough portions. Place on baking sheets coated with cooking spray. Cover and let rise 30 minutes or until doubled in size. Cut a 1/4-inch-deep "X" in the top of each roll.
Combine water and egg white; brush over rolls. Bake at 375° for 18 minutes or until golden brown. Remove from oven; immediately sprinkle with cheese. Serve warm.