1. For the dough, combine warm water and 1 teaspoon sugar in a small bowl; sprinkle yeast over top. Let stand 10 minutes until foamy; stir in 1 1/2 tablespoons olive oil.
2. Combine whole wheat flour, 3/4 cup all-purpose flour, 1 teaspoon salt and pepper in a large bowl. Stir in yeast mixture with a wooden spoon. Transfer dough to lightly floured surface, shape into a rough ball and knead 8 to 10 minutes, adding remaining 1/4 cup all-purpose flour if necessary, until smooth and elastic. Transfer to lightly oil bowl. Cover bowl with clean kitchen towel and let rise in a warm, draft-free place for 1 hour.
3. Twenty minutes before baking, adjust oven rack to lowest position. Place shallow baking pan on top rack of oven. Place baking stone on lowest rack and heat oven to 500 degree F.
4. Meanwhile, heat oven to 450 degree F. Wrap 4 large garlic cloves in foil. Bake 25 minutes, until softened. Cool; remove peel and mash to form a paste.
5. Heat grill. Combine 3/4 teaspoon salt and 1/2 teaspoon pepper in cup. Cut white mushrooms in half. Slice portobello mushroom caps 1/2 inch thick. Arrange mushrooms in a grill basket. Brush both sides of mushrooms with 1/4 cup olive oil; sprinkle with salt and pepper mixture. Grill mushrooms over medium heat 10 minutes, turning until tender. Chop when cool.
6. Sprinkle a cookie sheet with cornmeal. Divide dough into 4 pieces. Shape 2 pieces into 10x6-inch ovals as directed. Combine rosemary and thyme. Spread half the garlic paste and 1-1/2 teaspoons of the herbs on dough ovals; brush with 2 tablespoons olive oil. Divide half the chopped mushrooms over herbs, pressing gently into the dough. Bake 10 minutes until lightly browned. Transfer to cookie sheet; cover loosely and keep warm. Repeat with remaining dough, garlic paste, 1-1/2 teaspoons herbs, 2 tablespoons cooking oil and mushrooms.
7. Divide crumbled feta cheese over tops of flatbreads; sprinkle with the remaining herbs. Makes 16 slices.