Pour the oil into a Dutch oven fitted with a deep-fry thermometer. Place over medium-high heat and preheat to 400 degrees F. Line a baking sheet with paper towels and place a cooling rack on top.
Make the batter: Pour the cake mix into a large mixing bowl. Whisk in the flour and baking powder. Add the milk and eggs. Use a hand mixer to blend the wet ingredients into the dry, until the batter is smooth and free of any lumps. Scrape the batter into a pastry bag and snip a small hole in the tip.
Quickly squeeze the batter in a circular motion into the hot oil, creating a lacey round about 3 inches wide. Fry until golden brown, about 30 seconds per side. Gently remove from the oil and flip onto the cooling rack (they are fragile). Repeat to make 16 funnel cakes. They will become crispy as they cool.
Allow the ice cream to soften on the counter for about 5 minutes. Scoop the ice cream onto 8 funnel cakes. Top each scoop with another funnel cake and gently press down. Dust the ice cream sandwiches with confectioners' sugar and serve immediately.
Heads up - the oil needs to be really hot for these!