Preheat the oven to 350°F and grease an 18x13-inch half sheet pan. Stir the almond milk and apple cider vinegar together in a small cup and let it sit for 5 minutes to curdle slightly.
In a large bowl, whisk together the flour, sugar, baking soda, and salt.
In a medium saucepan over medium heat, combine the butter, water, cocoa powder, and espresso powder. Bring to a boil while whisking, then pour the hot chocolate mixture over the dry ingredients and whisk until smooth.
Whisk in the curdled almond milk, eggs, and vanilla until the batter is glossy and smooth. Pour it into the prepared pan and spread it into an even layer.
Bake for 18 to 22 minutes, until a toothpick inserted in the center comes out clean.
During the last few minutes of baking, melt the butter with the cocoa powder and almond milk in a saucepan over medium heat and bring it to a gentle simmer.Remove from the heat and whisk in the powdered sugar and vanilla until completely smooth, then stir in the pecans.
Pour the warm frosting over the hot cake right away and gently spread it to the edges. Let the cake cool for at least 1 hour so the frosting sets into a thin fudgy layer before slicing.