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.
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