Place an oven rack in the center position and preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan generously with butter or nonstick baking spray, getting into all four corners.
Add the 2 cups of flour and 2 cups of granulated sugar to a large mixing bowl. Whisk for about 30 seconds until evenly combined and there are no lumps.
Add the 1/2 cup of butter pieces, 1/2 cup of vegetable oil, 3 tablespoons of cocoa powder, and 1 cup of Coca-Cola to a 3-quart saucepan. Set over medium heat and whisk often as the butter melts. Bring to a gentle boil, about 4 to 5 minutes, then remove from heat.
Carefully pour the hot cola mixture over the flour and sugar and whisk for about 1 minute until smooth and glossy. Whisk in the buttermilk, then add the eggs one at a time, whisking well after each. Sprinkle the baking soda over the batter and whisk it in, then stir in the vanilla.
Add the mini marshmallows to the batter and gently fold them in with a rubber spatula until evenly distributed. Pour the batter into the prepared pan and scrape the bowl clean.
Slide the pan onto the center rack and bake for 30 to 35 minutes, until a toothpick inserted into a spot without a big melted marshmallow comes out with a few moist crumbs but no wet batter.
Place the powdered sugar in a medium mixing bowl and break up any large lumps. Add the second 1/2 cup of butter, the second 3 tablespoons of cocoa powder, and the 6 tablespoons of Coca-Cola to your saucepan. Heat over medium heat, stirring often, until the butter melts and the mixture just comes to a boil. Pour the hot mixture over the powdered sugar and whisk until completely smooth. Stir in the chopped pecans and vanilla.
Remove the cake from the oven and set it on a wire cooling rack. Pour the warm icing over the hot cake right away, working from the center outward. Use an offset spatula to gently spread the icing to the edges and corners.
Let the cake cool for at least 30 minutes so the icing can set. Cut it into 4 rows by 5 rows to make 20 squares. Wipe your knife clean between cuts for neat edges, and serve warm or at room temperature.