Start by preheating your oven to 350°F (175°C). While that warms up, line two baking sheets with parchment paper or silicone mats and set them aside.
In a large mixing bowl, combine the cake mix, eggs, and vegetable oil. Beat everything together for about 2 minutes, or until the dough is smooth and well mixed.
Pour the confectioner's sugar into a small bowl. Using a 1½ tablespoon cookie scoop, portion out the dough and roll each ball in the sugar until it's nicely coated all around.
Place the sugared dough balls on your prepared baking sheets, spacing them about 3 inches apart so they have room to spread.
Bake for 10 to 12 minutes, or until the cookies are lightly golden and puffed up. As soon as they come out of the oven, use a teaspoon (the measuring kind works best) to gently press a small indent into the center of each cookie. Let them cool on the pan for about 5 minutes.
While the cookies cool, melt your white chocolate chips or chunks in a microwave-safe bowl. Heat in 30-second bursts, stirring between each round, until smooth. If the chocolate seems too thick, stir in a little coconut oil or shortening to help loosen it up.
Once the cookies have slightly cooled and the chocolate is ready, spoon about ½ to 1 teaspoon of the melted white chocolate into the center of each cookie.
Let the chocolate set completely—this usually takes a little while at room temperature. Once set, store the cookies in an airtight container and enjoy!