In a stand mixer, combine 1 cup of warm water, 2 teaspoons of instant dry yeast, 1 tablespoon of granulated sugar, 2 tablespoons of extra-virgin olive oil, 1 teaspoon of table salt, 1 large egg, and 2 tablespoons of dried potato flakes. Mix on low speed until well blended for 2–3 minutes.

Gradually add 3 cups of bread flour and 1 cup total of shredded Monterey Jack and sharp cheddar cheeses while mixing. Knead with the dough hook for 6 to 7 minutes until the dough is smooth and pulls away from the bowl’s sides.

Transfer the dough to a lightly oiled bowl, cover with a damp cloth or plastic wrap, and allow to rise at room temperature for 30 minutes until doubled in size.

Turn the dough out onto a floured surface and divide it into four pieces. Shape each piece into a rectangle, fold edges in, and roll into logs. Place logs on a silicone mat.

Mix together 1 teaspoon of garlic powder, 2 tablespoons of grated Parmesan cheese, 1 teaspoon of dried oregano, and 1 tablespoon of dried parsley. Brush logs with water and sprinkle topping mix. Let rise for another hour.

Preheat your oven to 375°F. Score the tops of each roll with a sharp knife and sprinkle any remaining cheese on top.

Place the rolls in the oven and bake for 16 to 20 minutes until tops are golden brown.

Transfer rolls to a wire rack and let cool completely before slicing.