Make the cake: Preheat the oven to 350°. Coat an 8-in. square baking pan with cooking spray. Line the pan with parchment, leaving a 2-in. overhang on 2 sides, then spray parchment.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cardamom.
In a large bowl, beat the butter and sugar on medium-high, until light and fluffy, about 3 min. Beat in the egg until fully combined, then the sour cream and vanilla. Add the dry ingredients to the batter, and mix on low until just combined.
Spread the batter evenly into the prepared pan. Arrange peach slices in an even layer on top of the batter. Set aside while you make the meringue.
Make the meringue: In a large bowl, beat the egg whites on medium speed until foamy, about 30 sec. Add cream of tartar. Increase the speed to medium-high, and gradually add the sugar, beating until all sugar is incorporated and mixture is glossy and forms stiff peaks, about 7 min. Dollop the meringue evenly to cover the top of the cake batter.
Bake the cake until the meringue is dry and a wooden skewer inserted through the center comes out clean, 40 to 45 min. Let the cake cool in pan for 15 min. Then run a knife around the edge of the pan. Carefully remove the cake using the parchment overhang, and transfer to a wire rack to cool completely.
Meanwhile, make the peach compote: Combine all peach compote ingredients, and let the mixture sit while the cake cools.
Spoon the compote over the top of the cooled cake. Slice, and serve with more mint.
Recipe by Laura Rege.