Preheat the oven to 350°F. Grease a 9x13-inch baking pan and line it with parchment paper, leaving a slight overhang on the sides to allow for easy removal after baking.
Prepare the cake batter. In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until evenly combined. Set the dry mixture aside.
In a separate large mixing bowl, beat the granulated sugar and softened butter with an electric mixer on medium speed for 3 to 4 minutes, or until the mixture is light, pale, and fluffy.
Reduce the mixer speed to low. Add the vegetable oil, then add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully incorporated.
Add the dry ingredients and buttermilk alternately to the butter mixture, beginning and ending with the dry ingredients. Mix on low speed after each addition just until combined. Add the mini chocolate chips with the final portion of the flour mixture and stir gently until evenly distributed.
Transfer the batter to the prepared baking pan. Spread it evenly with a spatula, ensuring the batter reaches the corners of the pan.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center of the cake comes out clean or with a few moist crumbs. Allow the cake to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely before frosting.
Prepare the frosting. In a small saucepan over medium heat, combine the light brown sugar and water. Stir slowly until the sugar has fully dissolved. Remove from the heat and allow the syrup to cool.
In a large mixing bowl, beat the softened butter on medium speed until smooth and creamy. Scrape down the sides and bottom of the bowl as needed.
Reduce the mixer speed to low and gradually add the powdered sugar, mixing until fully incorporated and smooth.
Slowly drizzle the cooled brown sugar syrup into the frosting. Increase the mixer speed to medium and beat for approximately 2 minutes, or until the frosting is light and fluffy.
Add the pinch of salt and milk, then mix until the frosting reaches a smooth, spreadable consistency.
Spread the frosting evenly over the fully cooled cake. Sprinkle the top with the remaining mini chocolate chips.
Slice the cake into 16 servings and serve.