Preheat the oven to 350 degrees F.
Set the chicken breasts on a baking sheet. Drizzle with olive oil and sprinkle generously with salt and pepper. Transfer to the oven and roast until just beginning to brown on top, about 25 minutes (the chicken will finish cooking on top of the pizza). Let cool, then cut into 1/4-inch slices.
While the chicken cools, heat a grill pan over medium heat. Add a naan to the pan and weight it with a heavy skillet. Grill until nicely charred, 3 to 4 minutes; flip, and grill for another 3 to 4 minutes. Repeat with the remaining naan. Remove the naan to a work surface. Brush with olive oil, season with salt, and then spread with the jam. Top the pizzas with the sliced chicken.
Place the pizzas on a baking sheet fitted with a wire rack. Transfer to the oven and cook until the jam starts to caramelize and the chicken browns, about 10 minutes.
Remove from the oven and top with the sliced brie. Allow the cheese to melt from the residual heat for a minute or two. Season with coarsely ground black pepper. Cut each pizza into 6 slices and serve immediately.
Combine the peaches, sugar and ginger in a saucepan over medium heat. Cook, stirring every couple minutes, until the sugar melts and the peaches soften, 10 minutes. Add the moonshine, lemon juice and zest, and simmer until thickened, about 20 minutes, stirring every couple minutes to prevent scorching. Store in the refrigerator for up to 1 month.