Getting Ready: Adjust rack to lower-middle position and preheat oven to 350°F (180°C). Line a 9- by 13-inch anodized aluminum baking pan with parchment paper, covering bottom and long sides of pan. (It’s all right to leave the short sides exposed.) Lightly grease pan with nonstick cooking spray.
For the Syrup: In a 2-quart nonreactive saucepan over medium-high heat, simmer together sugar, apple juice, ginger, and lemon peel until syrup reaches 234°F (112°C) on an instant-read thermometer. Remove syrup from heat and add lemon juice and Applejack. Set aside and allow to cool to room temperature.
For the Flatbread: Combine flour, salt, yeast, and sugar in the bowl of a stand mixer and whisk until combined. Add olive oil and the yogurt or milk and knead with dough hook at low speed until dough comes together into a smooth ball. Dough should stick slightly to bottom of bowl as it kneads (add slightly more yogurt or milk as necessary). Continue to knead for 5 minutes. Alternatively, form dough in a food processor by adding all ingredients and processing until the dough rides around the blade. Transfer the dough to a clean bowl, cover tightly with plastic wrap, and allow to rise at room temperature until roughly doubled in volume, about 2 hours.
