Heat the oven to 350°. Coat a 12- by 17-inch rimmed baking sheet with cooking spray and dust with cocoa.
In a mixer, combine the flour, sugar, baking soda, and salt.
In a small saucepan over medium heat, combine 3/4 cup water, the butter, canola oil, and cocoa, whisking frequently, until melted and smooth.
Add the cocoa mixture to the flour mixture and blend on low for about 30 seconds. Add the buttermilk, vanilla, and eggs; mix well at medium speed for another 30 seconds. Pour the batter into the prepared pan.
Bake until the center springs back when touched, about 15 minutes.
While the cake bakes, make the frosting, whisking the butter, cocoa, and buttermilk in a small saucepan over medium heat until melted and smooth. Remove the pan from the heat. Gradually whisk in the confectioners' sugar and vanilla.
When the cake is done and still warm, spread the frosting over it, then sprinkle with pecans or peppermints. Let it cool in the pan on a wire rack. Cut into pieces, trimming off the cake's edges if they seem dry.
