Preheat oven to 350°F. Line baking sheets with parchment paper. In a medium-large bowl, stir flour and baking soda together. Set aside.

Beat butter, shortening, and sugars with your electric mixer on medium speed until pale and fluffy, about 1 minute. Beat in eggs, 1 at a time, and then vanilla extract. Reduce speed; gradually add flour mixture, and mix until just combined. Add animal cracker pieces and white chocolate chips and mix until combined.

Scoop dough using a medium-size cookie scoop. Roll tops and sides of cookies in nonpareils. Place on prepared baking sheets, 2 inches apart.

Bake for about 12 minutes, until edges are just barely golden. Immediately press a frosted animal cracker into the center of each cookie. Let cookies cool on baking sheets for several minutes, then remove to rack to cool completely.