1. Make cake: Preheat oven to 350ºF. Grease a 9-inch round cake pan; line with parchment paper. Grease parchment. Lightly coat bottom and sides of pan with flour, knocking out excess.
2. In a bowl, whisk flour, baking powder and salt. In a separate bowl, whisk milk, eggs and vanilla. Using an electric mixer on medium-high speed, beat butter and sugar until light, about 2 minutes. Lower mixer speed; beat in half of flour mixture. Beat in milk mixture, then remaining flour mixture. Increase mixer speed to medium-high; beat just until smooth.
3. Scrape batter into pan; smooth top. Bake until cake is light golden and starts to pull away from sides of pan, about 25 minutes. Cool in pan on wire rack for 15 minutes. Invert onto rack, peel away parchment, turn cake right side up and cool completely. Cut into 12 wedges. Place wedges on a parchment-lined baking sheet; freeze for 30 minutes.
4. Make frosting: Using an electric mixer on medium speed, beat shortening, butter and vanilla. Add confectioners' sugar, 1 cup at a time, beating well after each addition. Add milk; beat until frosting is fluffy.
5. Reserve 1 cup of icing in a small bowl. Divide remaining icing between 2 medium bowls and tint 1 bowl with yellow food coloring and 1 with orange.
6. Working with 1 wedge at a time, leaving remaining cake wedges in freezer, frost pointed end with white icing, middle portion with yellow icing, and outer portion with orange icing. Repeat with remaining cake wedges and frosting. Press sprinkles on outside of wedges, if desired. Chill until ready to serve.