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1
Adjust oven rack to middle position and preheat to 350°F. Line a 12-cup muffin tin with cupcake liners. Stir the butter, sugar, and salt in a large bowl until creamy. Whisk in the oil, then the egg, egg yolk, buttermilk, and red food coloring until well combined.
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2
Sift the flour, cocoa powder, and baking soda over the wet ingredients. Stir until just combined. Spoon evenly into the prepared muffin tin and bake until the centers are just set, 18 to 20 minutes. Let cupcakes cool in pan for 5 minutes, then remove to cool completely on wire rack.
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3
Set cupcakes on a small tray. Cut a cone shape out of the top center of each cupcake and reserve. Fill center with a scoop of ice cream and smooth the top. Set the cut-out cones on top of the ice cream on each cupcake (see note). Freeze until ice cream is firm, about 30 minutes.
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4
In an electric mixer fitted with the paddle, beat cream cheese and butter at medium speed until creamy in a mixer fitted with the paddle attachment. Add the sugar and beat at medium-high speed until light and fluffy, about 3 minutes.
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5
Spoon half of the frosting into a bowl and stir in drops of blue food coloring to desired color. Place each frosting in a bag fitted with a star tip.
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6
Pipe alternate layers of the colored frostings around the cone on top of each cupcake until it is completely covered. Freeze until firm, about 2 hours. If making ahead, place cupcakes in an airtight container and wrap well. Serve straight from freezer (see note).
