Preheat oven to 400°F. Butter a 13-by-18-inch rimmed baking sheet; set aside. In a small saucepan, bring cocoa powder and 1 cup water to a boil. Remove from heat; whisk in butter and mayonnaise.
In a medium bowl, whisk together sugar, flour, cinnamon, baking soda, and salt. In a large bowl, whisk together buttermilk, eggs, and vanilla. Stir in flour mixture until well combined. Add cocoa mixture and whisk until smooth. Transfer to prepared pan and spread to edges. Bake until cake springs back when lightly pressed and pulls away from sides of pan, 15 to 20 minutes. Let cool 20 minutes.
Melt butter in a medium saucepan over medium heat. Whisk in cocoa powder and buttermilk; bring to a simmer. Remove from heat and add confectioners' sugar and vanilla, whisking until smooth. Stir in half of pecans. Spread icing over cake while warm, then sprinkle with remaining pecans. Let cool completely.