Preheat oven to 350 degrees F (175 degrees C). Grease three 9-inch cake pans.
Combine flour, canola oil, white sugar, buttermilk, eggs, vinegar, baking soda, 1 teaspoon vanilla extract, and cocoa powder in a large bowl. Mix until evenly distributed, 2 to 5 minutes. Pour batter evenly into the prepared cake pans.
Bake in the preheated oven until golden brown, about 20 minutes. Remove from oven and let cool, about 30 minutes.
Combine sweetened condensed milk, dark brown sugar, butter, 2 teaspoons vanilla extract, and salt in a saucepan over medium heat. Bring to a boil. Stir constantly until frosting is thick, 3 to 5 minutes. Let cool, about 5 minutes.
Remove cooled cakes from pans. Spread frosting onto the cooled cake layers. Stack layers; frost top and sides.