Prepare the custard: In a medium saucepan, combine egg yolks, sugar, and cornstarch, whisking until smooth. Gradually add whole or coconut milk while stirring continuously. Heat over medium heat, stirring consistently for about 5-7 minutes until the mixture thickens and coats the back of a spoon. Once thick, remove from heat, stir in butter and vanilla extract, and pour into a bowl to chill in the refrigerator until firm, about 1 hour.

Make the mochi dough: In a heatproof bowl, mix glutinous rice flour and sugar until well combined. Gradually add milk, stirring until you achieve a smooth batter. Microwave in 1-minute intervals for about 3-4 minutes, stirring between each interval, until the mixture becomes thick and translucent. Once done, stir in melted butter and let the dough cool for approximately 10 minutes until it's manageable to touch.

Form mochi balls: Dust your hands and a clean surface with cornstarch to prevent sticking. Divide the cooled mochi dough into small portions. Take one portion, flatten it out, and place a chilled custard ball in the center. Wrap the dough around the custard, ensuring it's completely sealed, and roll it into a smooth ball. Repeat this process with the remaining dough and custard filling.

Coat and chill: Roll each mochi ball in crushed vanilla cookies to create a crunchy exterior. Place the coated mochi balls in mini cupcake liners for a pretty presentation if desired. Transfer them to the refrigerator and let chill for 20-30 minutes before serving.