Step 1

Place the eggs, 1 cup of the milk, and the sour cream in a medium bowl and let sit until they come to room temperature, about 30-45 minutes.

Step 2

Arrange a rack in the middle of the oven and preheat the oven to 350 degrees F.

Step 3

Coat a 9x13-inch baking dish with 1 tablespoon of the vegetable oil.

Step 4

In a large bowl, add the all-purpose flour, the brown sugar, the granulated sugar, 1/2 cup of the Dutch-processed cocoa powder, the baking powder, and the baking soda and whisk until combined.

Step 5

Add the remaining vegetable oil, 1 tablespoon of the vanilla extract, and 1/2 teaspoon of the kosher salt to the egg mixture and whisk until smooth and combined.

Step 6

Add the wet ingredient mixture to the flour mixture and stir with a wooden spoon or flexible spatula until just combined.

Step 7

Pour the batter into the prepared baking dish.

Step 8

Bake until a toothpick inserted into the center comes out clean, about 30-33 minutes.

Step 9

Transfer the cake from the oven and evenly scatter the marshmallows over the still-hot cake.

Step 10

Return the cake to the oven and bake just until the marshmallows start to melt, about 2-3 minutes.

Step 11

Place the baking dish on a wire rack and let the cake cool for 30 minutes.

Step 12

In a large saucepan over medium heat, melt the unsalted butter.

Step 13

Add the remaining milk, the remaining Dutch-processed cocoa powder, the remaining vanilla extract, and the remaining kosher salt to the melted butter and whisk until combined.

Step 14

Slowly sift in the powdered sugar and whisk until smooth, about 1 minute.

Step 15

Remove the saucepan from the heat and let the frosting cool.

Step 16

Slowly pour the frosting over the warm cake and spread it into an even layer.

Step 17

Let the cake sit until the frosting is set, about 30 minutes.

Step 18

Slice and serve.