1. Preheat the oven to 350°F, with a rack in the center position. Line an 18-by-13-inch rimmed baking sheet with parchment. Coat the sides and corners with nonstick cooking spray.

2. In a medium bowl, toss the fruit with the lemon juice, 2 tablespoons of the granulated sugar, and ¼ teaspoon of the cloves.

3. Into a large bowl, sift together the flour, baking powder, baking soda, 1 teaspoon of the cardamom, and the salt. Add the butter, yogurt, eggs, vanilla, and 1¼ cups of the granulated sugar and whisk well to combine. Sweep the bottom and sides of the bowl with a silicone spatula to dissolve any hidden pockets of flour.

4. Scrape the batter into the prepared baking sheet (it will be a very thin layer), smoothing the top and working the batter into the corners. Scatter the fruit in big spoonfuls evenly over the batter, drizzling any residual juice onto the cake. In a small bowl, stir together the remaining 1 tablespoon granulated sugar and the remaining ¼ teaspoon each cloves and cardamom. Sprinkle evenly over the batter. Bake for 35 to 45 minutes, until nicely browned and a skewer inserted in the center comes out clean. Cool completely on a rack.

5. Cut into 24 squares. Dust each square lightly with confectioners’ sugar just before serving. Spoon a dollop of Greek yogurt alongside each slice, if desired.