In the bowl of a stand mixer, beat the butter on medium speed until light and fluffy, about a minute. With the mixer on low, add the vegetable oil, sugar, and vanilla slowly and in succession after. Add the eggs one at a time and beat until well incorporated.
In a separate bowl, whisk together the flour, baking soda, and salt. Add to the wet ingredients in increments while the mixer mixes on low speed, until combined.
Add the 3 heaping tablespoons of sprinkles and mix until just combined. Refrigerate the dough for at least an hour, or pop in the freezer for 15-20 minutes.
Roll the chilled dough into roughly golf ball sizes and flatten just slightly with the palm of your hand. Bake in an oven heated at 350 degrees Fahrenheit for about 12 minutes, or until the center is just set and the edges are lightly golden.
To make the drizzle, fill a small sauce pan a quarter of the way with water, and find a glass bowl that will fit on top of it without touching the water. Turn the heat to medium high, and add the white chocolate, coconut oil (gives it a smooth consistency), and vanilla to the glass bowl. Stir occasionally as the mixture slowly melts down. Keep on the heat until all lumps have disappeared.
Lay the cookies evenly on a clean surface, preferably on top of wax or parchment paper for easy cleanup. Fill a parchment triangle with the white glaze mixture, or use a plastic storage bag and nip one of the edges. Drizzle over the top of all of the cookies. Add a few extra sprinkles on top if you like. If transporting the cookies, let the drizzle harden before layering on top of each other. Otherwise, enjoy immediately.