Preheat oven to 350°F degrees and grease a 9-inch pan. Place a parchment circle on the bottom.
Sift together flour, baking powder, baking soda, salt and ground vanilla beans. Reserve.
In a mixer, cream sugar, butter and lime zest until color is light yellow. Add eggs.
Add dry ingredients, alternating with yogurt. Do not over mix and scrape the sides and bottom, you want to have a homogenous batter.
Place in oven.
Meanwhile, over high heat pour coconut oil in a large saute pan and caramelize kiwi slices. Cool and coat both sides in sugar.
After 15 minutes of baking the cake, open the oven slowly and arrange kiwi slices. Do this quickly as to not lose all the heat inside your oven. Continue to bake until cake is set in the center and when you touch the top, it springs back softly.