Chocolate Fudge Layer Cake
['1 1/4 sticks (1/2 cup plus 2 tablespoons) butter, plus extra for greasing', '1 1/4 cups whole milk', '1/2 cup plus 2 tablespoons vegetable oil', '1 teaspoon vanilla extract', '2 3/4 cups all-purpose flour', '1/4 cup plus 2 tablespoons cocoa powder', '1 teaspoon baking soda', '2 teaspoons baking powder', '1/4 teaspoon salt', '1 1/2 cups light-brown sugar', '14-ounce can sweetened condensed milk', '1/2 cup plus 2 tablespoons heavy cream', '7 ounces bittersweet chocolate (50-70% cacao, depending on your taste), chopped', '1/2 stick (1/4 cup) butter, cubed', '1 teaspoon vanilla extract', 'Two 8-inch round cake pans']
Make the cake: Preheat the oven to 350F. In a small saucepan, gently melt the 1 1/4 sticks of butter. Remove from heat and whisk in the milk, oil, and vanilla. Meanwhile, grease two 8-inch round cake pans, then line the bottoms with circles of parchment paper.
Mix together the flour, cocoa, baking soda, baking powder, and salt, then sift into a large bowl.
Add the brown sugar and break up any lumps. Make a well in the center and add the butter mixture. Using a whisk, slowly mix the ingredients together, then give it a good beating until smooth and evenly blended. Using a spatula, divide the batter equally between the pans and spread it flat.
Bake until the cakes are risen, firm, and have shrunk back slightly from the edges of the pans. Let cool in the pans 10 minutes, then turn out onto a cooling rack and cool completely.
Make the frosting: In a medium saucepan, stir the condensed milk and cream over low heat until it starts to bubble at the edges. Remove from heat and stir in the chocolate, butter, and vanilla. Let the chocolate melt, stirring and beating occasionally as it cools, until thick, fudgy, and completely cooled.
Assemble the cake: On a cake plate lined with strips of parchment paper, sandwich the cakes together with 1/2 cup frosting. Spoon the remaining frosting over the top of the cake. Spread it out thickly, then, working on a quarter of the cake at a time, work the frosting over the edge of the cake and down to meet the plate. Try to keep going in one fluid movement. Repeat all over. Smooth and swirl the frosting as you like, or leave it rough.
Let the cake sit somewhere cool for an hour (or up to a day) before slicing.
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