Preheat oven to 350* F and pre-grease a 3 quart baking dish.
In a small bowl, toss chopped apples, grated zucchini, cinnamon, and 1 teaspoon of sugar until apples and zucchini are coated. Set aside.
Whisk together brown sugar, granulated sugar, butter, yogurt, and vanilla. Whisk by hand or with mixer for a minute or so, until mixture is smooth.
Add three eggs to the sugar mixture and again whisk well, until some bubbles form.
Add flour, baking powder, and salt to the mixture and mix well. It should be a very thick consistency. Fold apples and zucchini into the mixture until evenly mixed.
Pour mixture into pre-greased baking dish and smooth out evenly. Place onto the middle rack of the oven and bake for 45 minutes, or until lightly browned and a toothpick inserted into the center comes out clean. Allow to cool.
While the cake cools, make the caramel glaze by heating a small saucepan over medium-high heat and melting 1/4 cup butter. Add 1/2 cup brown sugar and 1 tablespoon milk. Bring the mixture to a simmer and reduce heat to low. Keep at a low simmer for 10 minutes, stirring regularly to keep from burning. Remove from heat and add vanilla.
Once the cake has cooled a bit (slightly warm is good, just not hot), pour the caramel mixture evenly over the cake and spread with a spatula if needed. Allow to cool for at least 15 minutes before serving.