Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, leaving a 2-inch overhang on each side for easy removal. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined. In another medium bowl, beat the butter, brown sugar, and vanilla extract with an electric hand mixer on medium-high speed for 2 minutes until smooth and fluffy. Add the eggs one at a time, beating well after each addition and scraping down the sides and bottom of the bowl to ensure a creamy texture. Add half of the flour mixture and mix on low speed just to combine. Stir in the yogurt, then add the remaining flour mixture and gently fold it in until just combined, leaving a few streaks of flour. Toss 2 cups of the chopped apples with cinnamon, then fold them into the batter. Pour the batter into the prepared pan and spread evenly. Scatter the remaining 1 cup of apples on top and drizzle about 2 tablespoons of caramel sauce over them. For the topping, mix the sugar and cinnamon together and sprinkle evenly over the apples. Bake for 35 to 45 minutes, or until a skewer inserted into the center comes out clean. Remove from the oven and transfer the pan to a wire rack to cool for at least 1 hour. Before serving, drizzle additional caramel sauce over the top.