Preheat oven to 350 °F.
Pour 1 C lukewarm water into a large mixing bowl and dissolve in 1 tablespoon of sugar. Sprinkle 1 tablespoon yeast over the surface and let it sit for 10 minutes or until the yeast is foamy and covering the water surface. This is a good time to start preparing the calzone filling ingredients.
Stir ¼ teaspoon salt, 2 teaspoon olive oil, 1 C whole wheat flour and 1 C all-purpose flour into the water. Once the flour is incorporated sprinkle ¼ C of all-purpose flour onto the counter, place the dough onto this flour, and knead the dough. You may need to add up to another ¼ C of all-purpose flour. The dough should become smooth and be a bit sticky but not sticking to the counter significantly. Do not knead for more than 2 minutes as the dough becomes tough.
Press the dough into a ball and place back into the mixing bowl. Cover with a damp towel (or paper towel) and let it rest for 10 – 15 minutes. This is a good time to continue preparing the calzone filling ingredients.
Now the dough is ready to roll. Cut into 4 even pieces. Roll each of the 4 pieces on a floured surface until the dough is about ⅛ inch thick.
Transfer the rolled-out dough onto a baking sheet lined with either parchment paper, silicone baking mat or corn meal (to prevent sticking). If you use corn meal, note that the top of the calzone will be covered in corn meal as well.