In bowl, whisk coconut with 1 tsp of the clementine zest. Set aside.
In food processor, pulse clementines until finely chopped.
In small saucepan, bring clementines and 1/4 cup of the sugar to boil. Reduce heat and simmer, stirring occasionally, until mixture reaches jam-like consistency and is reduced by half, about 7 minutes. Let cool completely, about 30 minutes.
In large bowl, beat together egg whites, remaining sugar and cornstarch until foamy. Stir in coconut mixture and clementine mixture. Let stand until liquid is absorbed, about 5 minutes.
Roll by 1 tbsp into balls. Arrange, 1 inch apart, on parchment paper–lined rimless baking sheets. Bake, 1 sheet at a time, in 300°F oven until bottoms are light golden, 20 to 25 minutes. Let cool completely on pans.
Drizzle with white chocolate; sprinkle with remaining clementine zest. Refrigerate until white chocolate is set, about 10 minutes. (Make-ahead: Store in airtight container for up to 3 days.)
Makes about 24 cookies.