How to Make It
In a small bowl, whisk the whole wheat flour with the all-purpose flour and salt. In a large bowl, combine the warm water and honey. Sprinkle the yeast over the water and let stand for about 5 minutes, until foamy. Stir in the olive oil and then the flour mixture. Gently knead the dough on a work surface until it forms a smooth, somewhat sticky ball. Lightly oil another bowl and add the dough. Cover with plastic wrap and let stand in a warm place until doubled in bulk, about 1 hour.
In a skillet, heat the 1 tablespoon of olive oil. Add the onion and cook over moderate heat until translucent, 4 minutes. Add the lamb and garlic and season with salt and pepper. Cook over moderately high heat, breaking up the meat with a wooden spoon, until the lamb is no longer pink, 3 minutes. Add the sun-dried tomatoes, red pepper paste and cumin and cook, stirring, for 1 minute. Remove from the heat and season with salt and pepper.
Preheat the oven to 450°. Arrange oven racks on the top and bottom thirds of the oven. Preheat a large rimmed baking sheet in the oven for about 5 minutes.
On a lightly floured work surface, punch down the dough and cut into 4 pieces. Roll each piece into a 6-inch round. Arrange the dough rounds on the preheated baking sheet, about 1 inch apart. Bake on the bottom shelf of the oven for 2 minutes. Spread the lamb topping over the dough, leaving a 1/2-inch border around the edges; brush the borders with olive oil. Crack an egg in the center of each pizza (if using) and bake on the top shelf of the oven for about 6 minutes, until the crust is crisp on the bottom, the egg white is firm and the yolk is runny. Scatter the parsley over the pizzas and serve hot.
Turkish red pepper paste, also known as biber salcasi, is available at specialty stores.