How to Make It
Preheat oven to 350°F. Prepare the Topping: Place butter in a 9-inch round baking pan, and place in preheated oven until butter is melted, 2 to 3 minutes. Tilt pan to coat sides with butter. Stir brown sugar into melted butter in bottom of pan until smooth, spreading it evenly on bottom of pan. Decoratively arrange cherries, cut-side down, and thyme sprigs on brown sugar mixture.
Prepare the Cake: Whisk together flour, thyme leaves, baking powder, baking soda, and salt in a medium bowl. Set aside.
Beat together brown sugar and butter in bowl of electric stand mixer fitted with a paddle attachment on medium speed until light and fluffy, about 3 minutes, scraping down sides of bowl as needed. Add egg and vanilla, beating until fully incorporated, about 1 minute. Add flour mixture and sour cream; beat on low until just moistened. Stir ingredients by hand until fully incorporated.
Dollop cake mixture over fruit, and spread evenly to sides of pan. Bake in preheated oven until a skewer inserted in center comes out clean, about 40 minutes. Let cool in pan 10 minutes; invert onto a large cake plate. Let cool 5 minutes before slicing. Sprinkle with more thyme leaves, and serve with whipped cream or ice cream.