1. Preheat the oven to 350ºF (180ºC.) Butter or oil a 9-inch (23 cm) cake pan and line the bottom with parchment paper.
2. Use a whisk to mix together the flour, baking powder, baking soda, and salt.
3. In a large bowl, whisk together the 1 1/2 cups sugar, yogurt, oil, eggs, lemon juice, and zest until smooth.
4. Mix about one-third of the dry ingredients into the yogurt mixture, then stir the rest in, in two batches, just until the dry ingredients are completely incorporated. Do not overmix. Scrape the batter into the prepared cake pan and bake for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
5. While the cake is cooking, toss the apricots, cherries, sugar, honey, wine, and extract in a baking dish. Cover tightly with foil and bake in a 350ºF (180ºC) oven until the fruit is soft and fully cooked through; depending on ripeness, it will take between 20 and 30 minutes.
6. Let the cake cool for about 15 minutes, then run a knife around the outside of it to loosen it from the pan, and tip the cake out of the pan. Remove the parchment paper and let the cake cool completely, right side up, on a wire rack.
7. To glaze the cake, mix the powdered sugar and lemon juice until smooth. Pour it in the center of the top of the cake. Use a spoon or spatula to spread it gently right to the end, then let the glaze drip down the side. Serve the cake with the apricot-cherry compote either warm or at room temperature, perhaps with vanilla ice cream.