Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the butter and sugar until light and fluffy, about 2 minutes.
Beat in the egg, egg yolk, and vanilla until well combined.
Add the baking soda and salt, mix until incorporated.
Mix in the instant pudding mix for 30 seconds.
With the mixer on low speed, gradually add the flour and mix until just combined.
Fold in the sprinkles with a spatula.
Drop rounded tablespoons of dough onto ungreased baking sheets, about 2 inches apart.
Bake for 8 to 12 minutes, until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for a minute, then transfer them to a wire rack to cool completely.