In a medium saucepan, whisk together the egg yolks, sugar, and cornstarch until smooth. Gradually mix in the whole milk, stirring continuously. Heat over medium heat, constantly stirring until the mixture thickens and coats the back of a spoon, about 8–10 minutes. Remove from heat, stir in the butter and vanilla extract, then transfer to a bowl and let it chill in the refrigerator for at least 30 minutes until firm.

In a large mixing bowl, combine the glutinous rice flour and sugar, mixing well. Gradually pour in the milk while stirring to form a smooth batter. Transfer the mixture to a microwave-safe dish and microwave on high for 3–4 minutes, pausing every minute to stir until the dough becomes thick and sticky. Carefully remove from the microwave, mix in the melted butter, and let it cool for a few minutes.

Dust your hands generously with cornstarch to prevent sticking. Divide the cooled mochi dough into small portions and flatten each piece in your palm. Place a chilled custard ball in the center of each flattened dough piece, then wrap the mochi around the custard, sealing it tightly. Roll the filled mochi balls gently in your hands to achieve a smooth appearance.

Roll each mochi ball in the crushed vanilla cookies to create a delightful crunchy coating. If desired, place the coated mochi balls in mini cupcake liners for an elegant presentation. Transfer the assembled mochi balls to the refrigerator and chill for 20–30 minutes to firm up before serving.