Preheat oven to 350°F. Prepare the topping: Coat a 9-inch round cake pan with cooking spray. Combine rhubarb, 1/2 cup granulated sugar, and cornstarch in a bowl. Toss to coat; set aside. Combine 1/4 cup butter, brown sugar, chopped thyme, 1/2 teaspoon ginger, 1/2 teaspoon cardamom, and 1/4 teaspoon salt in a saucepan. Cook over medium, stirring often, until butter is melted. Pour mixture evenly into prepared pan. Prepare the cake: Whisk together flours, baking powder, 1/2 teaspoon cardamom, 1/2 tea-spoon ginger, and 1/2 teaspoon salt in a bowl; set aside. Combine 3/4 cup granulated sugar, mayonnaise, and 2 tablespoons butter in the bowl of a stand mixer fitted with the paddle attachment; beat on medium speed until well incorporated and smooth, 4 to 5 minutes, stopping to scrape down sides of bowl as necessary. Add eggs, 1 at a time, beating well after each addition. Beat in zest and vanilla until just combined. Add flour mixture and sour cream alternately to granulated sugar mixture, beginning and ending with flour mixture, beating just until combined after each addition. Arrange coated rhubarb pieces in a single layer on butter mixture in pan, including any excess sugar from bowl. Pour batter into pan; smooth with a spatula. Gently drop pan on counter several times to remove air bubbles. Bake at 350°F until a wooden pick inserted in center comes out clean, 55 minutes to 1 hour. Cool in pan on a wire rack 20 minutes. Run a knife around edge of cake to loosen it from sides of pan. Place a serving plate upside down on top of cake; carefully invert pan onto plate. Let stand until cake releases from pan, about 5 minutes; carefully remove pan. Sprinkle cake with thyme leaves. Serve with yogurt.