Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat 1/2 cup softened butter and granulated sugar with an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add eggs one at a time, beating well after each addition. Mix in 2 teaspoons vanilla extract.
Alternately add the flour mixture and 1/2 cup milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 25 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely in the pan on a wire rack.
While the cake cools, prepare the frosting by beating 1/2 cup softened butter until creamy.
Gradually add powdered sugar, 1 teaspoon vanilla extract, and 2 tablespoons milk. Beat until smooth and fluffy.
Once the cake is completely cool, crumble it finely into a large bowl.
Add the frosting to the cake crumbs and mix thoroughly until the mixture is well combined and holds together when pressed.
Roll the mixture into 1-inch balls and place them on a baking sheet lined with parchment paper.
Freeze the cake balls for 30 minutes to firm up.
Melt the white chocolate in a microwave-safe bowl in 30-second intervals, stirring between each, until smooth.
Using a fork or dipping tool, dip each cake ball into the melted white chocolate, coating completely. Allow excess chocolate to drip off.
Place the coated truffles back onto the parchment-lined baking sheet.
Refrigerate the truffles for at least 30 minutes or until the chocolate is set.
Serve chilled or at room temperature.