Preheat the oven to 350F/175C. Prepare a greased 9x13 inch pan.
Add the butter to a microwaveable bowl. Melt the butter in the microwave on high in 30-second intervals until completely melted (be careful the bowl might be hot).
Add the chocolate chips to the hot butter and mix until melted and fluid. Set aside.
Mix together the flour, cocoa powder, salt, and baking soda into a separate mixing bowl. Add the sugar, chocolate mixture, vanilla, eggs, condensed milk, vinegar, and mix until fully combined.
Add the cake batter evenly to the prepared pan.
Bake 25 minutes. Check it after 25 minutes with a cake tester inserted into the center. then check again after in 5-minute intervals.
Remove from the oven and set aside to cool.
For The Frosting
Prepare the icing right away, melt the butter with the chocolate chips in a medium-size saucepan. Sift in the cocoa powder. Add the milk, vanilla, and salt. Stir in the cocoa powder sugar. Mix until smooth.
Remove from heat and pour the icing over the warm cake. Spread the icing with a spatula if needed. Let the cake and frosting cool before serving.
Use good quality chocolate The better the quality the better the taste.
Use unsweetened cocoa powder the darker the cocoa powder the richer chocolate flavor.
Be sure the chocolate/butter mixture is not added too hot (or it will cook the eggs). The bowl should be just warm to the touch.
Use Sweetened Condensed Milk or use unsweetened with an extra tablespoon of sugar.
Don't have Condensed Milk? You can even use buttermilk instead, but be sure to omit the vinegar.
Don't overmix the batter just mix until combined.
Don't overbake or it will dry out this cake. Check it after 25 minutes with a cake tester inserted into the center, then check again after in 5-minute intervals.
Prepare and spread the frosting while the cake and frosting are still warm. They will cool together and the icing will set as it cools.