Set the oven to 350°F and line an 8x8-inch square pan with parchment paper for easy cleanup.
Begin by measuring the dried cherries, crystallized ginger, and dried apple. For the cherries and ginger, dice some, halve some, and leave some pieces whole. Use dried apple slices and cut them into smaller pieces—any type of dried apple will do. Set the dried fruit and ginger aside for later.*If you'd like cherry, ginger, and apple pieces on top of the bars, reserve a tablespoon or two of each to sprinkle over before baking. In a small bowl, combine the flour, baking powder, and ground allspice. Whisk them together and set the bowl aside.
In a medium bowl, combine the melted butter, cane sugar, and brown sugar. Whisk together until smooth and well blended, about one minute.
Mix the yogurt and vanilla extract into the butter mixture, whisking thoroughly for about 30 seconds until smooth and well combined.
Combine the dry ingredients with the wet ingredients and whisk until no traces of flour remain. Add the dried cherries, crystallized ginger, and dried apple, folding gently until evenly mixed.
Spread the batter evenly in the prepared pan. Top it with the reserved dried cherries, crystallized ginger, and dried apple pieces.
Bake the bars for 25 to 28 minutes, until they are lightly browned and a toothpick inserted in the center comes out clean. Allow them to rest in the pan for 10 to 15 minutes before moving them to a cooling rack.
After cooling to room temperature, cut the bars into slices and serve. Keep the bars in an airtight container at room temperature.