01 - Combine water, yeast, sugar, oil, salt, egg, and dried potato flakes in a stand mixer bowl and stir until well mixed.
02 - Add flour and both cheeses. Mix on low speed with dough hook for 1-2 minutes until combined, then increase to medium speed for 6-7 minutes. Dough should pull away from sides of bowl; add additional flour in 1-2 tablespoon increments if needed.
03 - Transfer dough to an oiled large mixing bowl. Cover and let rest at room temperature for 30 minutes.
04 - Turn dough onto lightly floured surface and divide into 4 equal pieces. Working with one piece at a time, press into a ~6"x11" rectangle. Fold lengthwise like a letter, then roll to create an 11-12" log. Place on a silicone sub roll mat on a baking sheet. Repeat with remaining dough.
05 - In a small bowl, combine garlic powder, Parmesan cheese, oregano, and parsley.
06 - Brush dough tops lightly with water and sprinkle herb mixture evenly over each loaf.
07 - Spray tops with nonstick baking spray and cover lightly with plastic wrap. Let rise at room temperature for one hour or until doubled in size.
08 - Heat oven to 375°F.
09 - Cut 3 diagonal slices approximately ½" deep on top of each roll. Sprinkle Monterey Jack and cheddar cheeses evenly over the loaves.
10 - Bake for 16-20 minutes until rolls are light golden brown.
11 - Transfer rolls to a wire rack and cool completely before slicing.