Combine the water, milk , oil, eggs, sugar, salt, garlic powder, garlic, rosemary, thyme and yeast in the bowl of a stand mixer. Add 2 cups of the flour and stir with a wooden spoon until the dough forms a rough, shaggy mass.
Attach the dough hook to the mixer, turn to medium-low speed, and gradually add the remaining flour, kneading until a mass of dough begins to form. Only add as much flour as needed to bring the dough together. Continue kneading on medium-high speed for 4 to 5 minutes until a soft, smooth ball of dough is formed. The dough should feel elastic and slightly tack to the touch. Only add additional flour if the dough is unbearably sticky.
Lightly spray a large clean bowl with cooking spray and place the dough in the bowl. Cover the bowl lightly with plastic wrap. Let rise for 1 hour at room temperature or until the dough is big puffy, and about doubled in size.
Spray a 13×9-inch baking pan with cooking spray. Gently deflate the dough. Use a bench scraper, knife or pizza wheel to divide the dough into 15 equal pieces.
Shape each piece into a tight ball and place in the prepared pan. Lightly cover the dough with plastic wrap and the rolls rise for 1 hour, or until about doubled in size.
Preheat the oven to 375 degrees F. In a small bowl whisk the egg then gently brush over risen rolls. Sprinkle the rolls evenly with the parmesan cheese.
Bake the rolls for 20 minutes, or until golden brown. Serve warm.