Prepare the Cake Batter
Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until well combined.
In another bowl, combine the milk, vegetable oil, vanilla extract, and eggs. Mix until smooth.
Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Do not overmix.
Divide the batter in half. In one half, stir in the cocoa powder until fully incorporated to create the chocolate batter.
Bake the Cakes
Using a piping bag or a spoon, alternate dollops of the vanilla and chocolate batter on the prepared baking sheets, creating a striped pattern.
Bake in the preheated oven for 12-15 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the cakes cool on the baking sheets for 5 minutes before transferring them to a cooling rack.
Make the Cream Filling
In a mixing bowl, combine the cold heavy cream, powdered sugar, and vanilla extract.
Using an electric mixer, whip the cream until stiff peaks form. This will create a fluffy filling.
Assemble the Zebra Cakes
Once the cakes are completely cool, spread a generous layer of the whipped cream filling on the flat side of one cake.
Top with another cake, flat side down, to create a sandwich. Repeat with remaining cakes.
Prepare the Chocolate Glaze
In a microwave-safe bowl, combine the chocolate chips and vegetable oil.
Microwave in 30-second intervals, stirring in between, until the chocolate is fully melted and smooth.
Glaze the Cakes
Dip the tops of each assembled cake into the melted chocolate glaze, allowing excess to drip off.
Place the glazed cakes back on the cooling rack to set for about 15 minutes.
For best results, ensure all ingredients are at room temperature before starting. Store the cakes in an airtight container in the refrigerator for up to 5 days.