Preheat oven to 350 degrees F. In a large bowl, combine the flour, sugar, cocoa, baking soda and salt. Mix very well and pour into a single layer in an ungreased 9×13 baking dish. Create three wells with your fingers down the center of the flour mixture (going lengthwise).
Pour the vegetable oil in one well, the vinegar in another and the vanilla in the last. Stir loosely. Add the water and stir until mixture is free of lumps. Place in the preheated oven and bake for 25-35 minutes, or until a toothpick inserted into the center comes out clean.
MAKE THE FROSTING
While the cake is baking, add the brown sugar, butter, milk, salt and vanilla to a medium saucepan. Bring to a boil over medium-high heat, stirring constantly. Let boil for 1 minute (still stirring), remove from heat and pour into a heat-proof bowl. Place the bowl in the fridge until the frosting is firm, about 20 minutes. Whisk until smooth.
ASSEMBLE THE CAKE
Spread the cooled frosting onto the cake and top with chocolate chips.
Refrigerate until the frosting is firm, about 20 minutes.