Prepare the Ice Cream: Line a rimmed baking sheet with parchment paper. Place softened ice cream in a large bowl; stir in candy. Spread ice cream into the prepared baking sheet. Cover with parchment paper, and freeze until solid, about 1 hour.

Meanwhile, prepare the Funnel Cakes: Fill a 12- to 14-inch cast-iron skillet halfway with canola oil. Heat oil over medium-high to 375°F, and maintain temperature throughout frying.

Whisk together flour, sugar, baking powder, and salt in a medium bowl. Whisk together milk, vanilla, and eggs in a small bowl. Add milk mixture to flour mixture, and whisk until well combined. (A few small lumps are okay.) Pour batter into a large squeeze bottle with a 1/4-inch opening or a wet measuring cup with a spout.

Hold bottle 1 to 2 inches above hot oil, and squeeze about 1/4 cup batter into oil in a circular motion, crossing over lines to create a 4-inch cake. Repeat process twice, to make 3 cakes. Fry cakes until golden brown, about 2 minutes per side. (Fry no more than 3 funnel cakes at a time to help control oil temperature.) Drain cakes on paper towels. Repeat process with remaining batter to make 14 cakes, making sure oil returns to 375°F between batches. Cool cakes completely before assembling, about 20 minutes.

Assemble Ice-Cream Sandwiches: Cut frozen ice cream into 7 (4-inch) rounds. Reserve remaining ice cream for another use. Place each ice cream round between 2 funnel cakes. Sprinkle with powdered sugar, and serve immediately.