This rich, dense chocolate cake, also often called a pie, is adapted from “New Southern Cooking” by Nathalie Dupree, an award-winning author of eleven cookbooks about the American South. Ms. Dupree says that the cake's top should be cracked and dry-looking like Mississippi mud in the hot dry summer, from which it gets its name. It is covered with a buttery cocoa and pecan icing to really take it over the top. Similar recipes, like the Muddy Fudge Pie, were likely named after this classic dessert. 
CAKE RECIPE HELP

INGREDIENTS
Cake:
2 cups sugar
1 cup (2 sticks or 16 tablespoons) unsalted butter
4 large eggs
1 1/2 cups unbleached all-purpose flour; spoon into measuring cup and level to rim
1/2 cup cocoa powder, natural or Dutch-process; spoon into measuring cup and level to rim
1/4 teaspoon salt
1 tablespoon vanilla
1 cup pecans, chopped

Icing:
1 pound or 4 cups powdered sugar
1/3 cup cocoa powder, natural or Dutch-process; spoon into measuring cup and level to rim
1 cup (2 sticks or 16 tablespoons) unsalted butter, melted
1 teaspoon vanilla
1 cup pecans, chopped
2 tablespoons whole or 2% milk

INSTRUCTIONS
Cake or Pie:
1. Position and oven shelf to the middle of the oven. Preheat the oven to 350 degrees F.

2. Butter a 9- x 13-inch pan. Cut out a piece of greased parchment paper to fit the bottom of the pan (don't skip this step). Set aside.

3. With stand mixer fitted with a paddle attachment, beat the butter until softened. Add the sugar at the side of the bowl, and beat together until light and fluffy.

4. Add the eggs, one at a time, beating after each addition. Add the flour, cocoa, salt, vanilla, and nuts, and beat again.

5. Turn the batter into the pan and bake for 25-30 minutes. Remove from the oven and cool on a rack. When cool, remove from pan and peel off the wax paper.

Icing:
Sift the sugar and cocoa together. Beat in the melted butter, vanilla, pecans and milk. When smooth, spread the icing over the cake.