Place a rack in middle of oven; preheat to 325°. Lightly coat an 8" or 9" square baking pan with nonstick vegetable oil spray. Line bottom with parchment paper and lightly coat parchment with nonstick spray.

Melt ½ cup (1 stick) unsalted butter in a small saucepan over medium-low heat, about 3 minutes. Transfer to a blender; reserve pan.

Add 2 large eggs, one 14-oz. can condensed milk, 2½ cups fresh (or frozen, thawed) corn kernels (from about 3 cobs), ½ cup milk, 1 Tbsp. vanilla bean paste or vanilla extract, and 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt and blend until mostly smooth with no whole pieces of corn left, about 4 minutes.

Whisk 2 cups (302 g) mochiko (sweet rice flour) and 1½ tsp. baking powder in a large bowl to combine. Add purée and whisk until combined and smooth, about 2 minutes. Scrape batter into prepared pan and smooth surface with offset spatula if needed.

Bake cake until just set and top is light golden around the edges, 40–45 minutes.

Just before cake is done baking, bring ¼ cup (50 g) sugar, 3 Tbsp. unsalted butter, 1 Tbsp. milk, and a large pinch of kosher salt to a simmer in reserved saucepan over medium heat, stirring constantly, and cook (still stirring) until sugar is dissolved, about 2 minutes. Remove from heat. Stir in ⅔ cup unsweetened coconut flakes.

Remove cake from oven and immediately pour topping over. Using an offset spatula, smooth across surface to cover evenly, spreading all the way to the edges.

Return cake to oven and bake until topping is golden brown, 15–18 minutes.

Transfer pan to a wire rack and let cake cool 20 minutes in pan. Turn cake out onto rack and let cool completely. Cut into squares to serve.