How to Make It
Preheat oven to 350°F. Prepare the Topping: Using a channel knife, cut strips of peel from lime; set aside. Place butter in a 9-inch square 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 pineapple slices and lime peel strips on brown sugar mixture.
Prepare the Cake: Whisk together flour, lime zest, baking powder, baking soda, and salt in a medium bowl. Set aside.
Beat together butter and brown sugar in a bowl with an electric stand mixer fitted with paddle attachment on medium speed until light and fluffy, about 3 minutes, scraping 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; serve with whipped cream or ice cream.