Prepare the Sheet Cake: Preheat oven to 350°F. Grease and flour a 9- x 13-inch baking pan. Beat eggs, cake mix, sour cream, melted butter, and vanilla extract with a stand mixer fitted with a paddle attachment on low speed until dry ingredients are just moistened, about 1 minute. Increase speed to medium. Beat until batter is smooth, about 2 minutes, stopping to scrape down bottom and sides of bowl as needed. Spoon batter into prepared pan; spread into an even layer. Bake in preheated oven until a wooden pick inserted in center comes out clean, 20 to 22 minutes. Cool in pan on a wire rack 20 minutes.
Meanwhile, prepare the Nehi Orange Curd: Beat sugar and butter with an electric mixer on medium speed until blended, about 1 minute. Add eggs and egg yolks, 1 at a time, beating until just blended after each addition. Gradually add soft drink and lemon juice to butter mixture, beating on low speed until just blended; stir in orange zest. (Mixture will look curdled.) Transfer mixture to a heavy 4-quart saucepan. Cook over medium-low, whisking constantly, until mixture thickens and coats the back of a spoon, 14 to 16 minutes. Remove from heat; stir in food coloring gel. (Use while mixture is still hot or very warm.)
Using a wooden dowel or round handle of a wooden spoon, poke holes over entire cake surface (spaced 1 to 2 inches apart), being careful not to poke all the way to the bottom. Pour warm curd mixture over cake, being sure to fill all holes and smoothing excess curd mixture evenly over surface. Let stand 30 minutes. Transfer to refrigerator; chill until completely cool, about 1 hour.
Prepare the Mascarpone-Whipped Cream Frosting: Whisk together mascarpone cheese, sugar, vanilla, and 1/4 cup of the heavy cream in a large bowl until just blended. (Don’t overmix.) Beat remaining 1 3/4 cups heavy cream with an electric mixer on medium-high speed until stiff peaks form, about 1 minute. Gently fold whipped cream into mascarpone mixture.
Spread frosting evenly over chilled cake; chill until ready to serve. Garnish with orange slices just before serving.