Grease a 9 x 13-inch (23 x 33 cm) baking dish with 2 tablespoons (30 mL) of extra virgin olive oil.
In the bowl of a stand mixer fitted with a paddle attachment, combine the warm water, whole wheat flour, all purpose flour, instant yeast, dried basil, dried oregano, and salt. Beat over high speed for about 1 minute or until all of the ingredients have been evenly incorporated. The dough will be sticky.
Lightly oil your hands so the dough is easier to work with. Scoop the dough out of the bowl and transfer to the greased baking dish. Press and spread the dough out - it does not need to reach the corners perfectly as once it rises, this will naturally occur.
Cover the baking dish with a clean shower cap or plastic wrap and set in a warm, dry place and let the dough rest for 60 to 90 minutes, or until it is puffy and has filled out to the edges of the pan.
Preheat oven to 375°F (190°C) with a rack in the center position. Once dough has proofed, drizzle the top of the dough evenly with the remaining 2 tablespoons (30 mL) of extra virgin olive olive oil and gently poke the dough with your fingers, distributing it evenly. Sprinkle on the grated cheddar cheese, if using.
Bake until golden brown, roughly 35 to 40 minutes. Sprinkle lightly with flake salt, such as Maldon. Cut and serve warm.