Nowruz Bake: Lime Coconut Cake

Another Smitten Kitchen production:

1 cup sweetened flaked coconut
8 tbsp unsalted butter, softened
1 1/4 cups sugar
1 tablespoon lime zest
2 large eggs
1 3/4 cups flour
1 heaping tsp baking powder
1 scant tsp salt
3/4 cup whole milk
1/4 cup lime juice, divided
1 cup powdered sugar

Preheat oven to 350. Grease 9-inch square springform pan. Toast coconut in a small baking pan in oven, stirring once or twice, until golden, 5-7 minutes (burns easily---buy extra coconut!). Beat together butter, sugar, and zest until fluffy. Beat in eggs one at a time. Stir together flour, salt, baking powder, and 1/2 cup coconut. Stir together milk and 2 tablespoons lime juice (no idea why the recipe does it---it just curdles the milk). At low speed, mix flour and milk mixtures into egg mixture alternately in batches. Spoon batter into pan and smooth top. Bake until toothpick comes out clean, 40 to 45 minutes. Cool to warm. Whisk powdered sugar with remaining lime juice and spread on warm cake. Top with remaining coconut.