Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper leaving a 2-inch overhang at each side.
Combine flour, baking powder, baking soda and salt in a medium bowl and whisk to blend evenly.
Combine butter, brown sugar and vanilla in a medium bowl and beat with an electric hand mixer for 2 minutes on medium-high speed until smooth and fluffy. Beat in eggs one at a time, blending well after each addition and scraping down the sides and bottom of the bowl until it looks creamy. Add half of the flour mixture and mix on low to combine. Mix in yogurt. Add remaining flour mixture and fold it in until just combined but there are a few streaks of flour. Toss apples with cinnamon and add 2 cups to the bowl over the batter, then fold it in.
Spread batter into prepared pan and then scatter remaining 1 cup of apples on top. Drizzle about 2 tablespoons of caramel sauce over the apples.
For the topping, blend together sugar and cinnamon and sprinkle it over top. Bake for 35-45 minutes until a skewer inserted into the center comes out clean. Transfer to a wire rack and let cool for at least 1 hour, then drizzle caramel sauce over top before serving.