How to Make It
Make the dough Brush a large bowl with olive oil. In the bowl of a stand mixer, whisk 1 1/4 cups of water with the yeast and sugar and let stand until foamy, about 5 minutes. Add the 3 cups of flour, the salt and the 1 tablespoon of olive oil. Attach the paddle to the mixer and beat at medium-low speed until a dough forms. Switch to the dough hook and knead at medium speed until the dough is smooth, about 5 minutes. Transfer the dough to the prepared bowl, cover with plastic wrap and let rise in the refrigerator until doubled in bulk, 24 to 48 hours. Let the dough rest at room temperature for 1 hour before baking.
Meanwhile, make the sauce In a medium saucepan, heat the olive oil. Add the garlic and jalapeño and cook over moderately low heat, stirring occasionally, until softened, 2 to 3 minutes. Add the crushed tomatoes, sugar and 1/2 cup of water and simmer over moderately low heat, stirring occasionally, until thickened, about 25 minutes. Strain the sauce through a sieve, pressing on the solids; discard the solids. Return the sauce to the pan, add the basil and simmer over moderate heat for 10 minutes. Discard the basil; season with salt and pepper.
Prepare the toppings In a large skillet, heat the olive oil. Add the onion and cook over moderate heat, stirring occasionally, until lightly browned, 8 to 10 minutes. Stir in the baharat and 2 teaspoons of the garlic and cook, stirring, until softened, about 2 minutes. Add the lamb and cook, breaking up the meat with a spoon, until no pink remains, about 6 minutes. Using a slotted spoon, transfer to a paper towel–lined plate, then transfer to a medium bowl. Season with salt and pepper.
In a medium bowl, toss the diced tomatoes with the chopped mint, lemon juice and remaining 1 teaspoon of garlic. Season with salt and pepper.
Put a pizza stone in the oven and preheat to 500°, at least 30 minutes. Cut the dough into 6 pieces and roll them into balls. On a lightly floured work surface, dust the balls with flour and let rest for 10 minutes. Work with 1 piece of dough at a time: On a floured inverted baking sheet, stretch a ball of dough into an 8-inch round. Spread 2 tablespoons of the sauce on the dough, leaving a 1/2-inch border. Top with a scant 2/3 cup of the lamb mixture.
Carefully slide the pie onto the pizza stone and bake for 6 to 7 minutes, until the edges of the crust are golden and crisp. Transfer to a plate. Repeat with the remaining dough, sauce and lamb. Top the pies with some of the tomato salad. Garnish with mint leaves and serve.
Baharat spice blend commonly includes black pepper, cumin and cinnamon, and is available at kalustyans.com.