Preheat oven to 350 degrees F.
Grease a 9-inch square baking pan, then line with parchment paper; set aside.
Stir together vanilla wafer crumbs, the melted butter, and 2 Tablespoons sugar. Press into the bottom of the prepared pan. Bake until the crust is just brown around the edges, 8 to 10 minutes.
Meanwhile, beat the cream cheese with a mixer on medium speed until fluffy, about 2 minutes. Add the remaining 3/4 cup sugar and beat for an additional couple of minutes, until smooth.
Add the eggs and yolk, 1/2 cup + 2 Tablespoons milk, vanilla, salt and beat again until completely combined and smooth.
Finally, stir in the cake mix and sprinkles until smooth.
Pour the filling over the crust. Set the pan in a larger pan (a 9 × 13-inch works for this), and add enough hot water to come halfway up the sides of the baking pan.
Bake until just set, 40 to 45 minutes. Remove the baking pan from the water bath, and transfer to a wire rack. Let cool for 30 minutes, then refrigerate for at least 3 hours or overnight.
Cut into bars. Store leftovers in an airtight container in the refrigerator.