In small food processor (like this KitchenAid on Amazon), finely grind the sweetened coconut with the granulated sugar, flour, and salt. Transfer to a large bowl and set aside.
In a large bowl, whisk the egg whites until very frothy. Dump the egg whites over the dry ingredients, along with the cooled brown butter, and the vanilla. Fold everything together until you obtain a thick batter.
Cover the bowl with plastic wrap and let the batter chill for 30 minutes.
Preheat the oven to 350 °F (175 °C). Butter and flour 16 cups of a mini muffin pan (like this push pop pan on Amazon). When the batter has chilled, divide between the prepared cups. Cut the kiwifruit in half, and scoop out the flesh. Slice into 16 slices. Top each coconut financier with a slice of Zespri SunGold kiwifruit.
Bake on the middle rack for 20–25 minutes, until the edges are golden and a skewer inserted into a cake comes out clean. Let cool 10 minutes before unmolding to a wire rack to cool completely