Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan thoroughly with butter or coconut oil, then line with parchment paper, leaving overhang on two sides for easy removal.
Toast 1 cup of the shredded coconut on a baking sheet for 5-7 minutes until golden brown, stirring once halfway through. Set aside to cool completely.
In a large mixing bowl, whisk together the sweet rice flour, sugar, and salt until no lumps remain.
In a separate bowl, whisk the eggs until smooth, then add the coconut milk, whole milk, melted butter, and vanilla extract. Whisk until completely combined.
Pour the wet ingredients into the dry ingredients and whisk vigorously for 1-2 minutes until you have a smooth, slightly thick batter with no flour pockets visible.
Fold in the remaining 1/2 cup untoasted shredded coconut until evenly distributed throughout the batter.
Pour the batter into the prepared pan and spread into an even layer. Bake for 60-70 minutes, until the top is golden brown and the center jiggles slightly but doesn't slosh when you gently shake the pan.
Remove from the oven and let cool in the pan on a wire rack for at least 2 hours, or refrigerate for 1 hour until completely set and cool to the touch.
Use the parchment overhang to lift the mochi block onto a cutting board. Cut into 24 squares using a lightly oiled knife or plastic bench scraper, wiping the blade clean between cuts.
Roll each square in the toasted coconut, pressing gently so it adheres to all sides. Arrange on a serving platter and enjoy immediately or store in an airtight container.
