In a microwave-safe bowl, whisk together the glutinous rice flour, cornstarch, sugar, milk, and food coloring until smooth. Cover the bowl with plastic wrap, poke a few holes with a toothpick, and microwave for 3 minutes. Remove the bowl, add the butter, and stir until incorporated. Transfer the dough to a stand mixer fitted with a dough hook and knead for 3–4 minutes, until smooth and elastic. Let cool completely.

In a mixing bowl, beat the whipping cream, sugar, and mango puree on medium speed until soft peaks form. Add the pudding mix and continue whipping until the cream is stable and holds its shape.

Lightly dust a clean surface with cornstarch. Divide the cooled dough into 9–10 equal portions. Roll each piece into a circle, about 3 inches in diameter. Place a circle of dough in a small bowl, spoon or pipe the mango cream into the center, and lightly dampen the edges of the dough with water. Carefully pinch the edges together to seal, trimming any excess dough with scissors if needed. Dust the seam with a little more cornstarch.

Arrange the filled mochi on a parchment-lined tray and freeze for at least 1 hour, or until the filling is semi-frozen. Let sit at room temperature for 5 minutes before serving.