In a medium saucepan, whisk together the egg yolks, sugar, and cornstarch until smooth. Gradually pour in the whole milk while whisking. Cook over medium heat, stirring constantly until thickened and bubbling for about 5-7 minutes. Remove from heat, stir in butter and vanilla extract, then chill for 30 minutes.

In a large mixing bowl, combine glutinous rice flour and sugar. Gradually add milk to form a smooth batter. Transfer mixture to a microwave-safe bowl and heat in 1-minute intervals, stirring until thick and sticky, about 3-4 minutes. Mix in melted butter and let cool slightly.

Dust hands with cornstarch, take small pieces of mochi dough, flatten into discs, place a custard ball in the center, wrap the dough around and seal completely. Shape into smooth balls.

Roll each mochi ball in crushed vanilla cookies and refrigerate for 20-30 minutes until firm. Serve chilled or store in an airtight container.