In a standing mixer with dough hook, combine whole-wheat flour, all-purpose flour, yeast, salt, and sugar. With the motor running, gradually add oil and water. Knead on low speed until dough is firm and smooth, about 10 minutes.
Divide dough into four balls. Line two cookie sheets with parchment paper. Place two balls on a sheet and cover with a damp towel. Let them rise in a warm spot until they have doubled in bulk, about 2 hours.
Extra-virgin olive oil
4 scallions, thinly sliced
¼ cup Parmigiano-Reggiano cheese
Heat your grill to medium-high, and oil the grates lightly. Roll dough out as thinly as possible. Place dough on grates and cook about 1 minute, or until very lightly browned.
Turn dough over and quickly spread about ½ cup tomato sauce over dough. Add mozzarella rounds. Cover grill. Let cook about 2 minutes and check; edges should be browned and cheese softened. Cook longer if necessary.
Transfer to a cutting board. Drizzle with olive oil, scallions, and cheese. Cut and serve.
In a small saucepan over medium-low heat, cook garlic gently in olive oil, 4 minutes, being careful not to brown. Add pepper flakes and cook 1 more minute. Add tomatoes and juice and stir well. Raise heat to simmer; cook, stirring often, about 10 minutes.