If you haven't done so, bake the flour at 350℉ for 3-5 minutes or microwave for 1 minutes, stirring every 15 seconds. This will kill any bacteria that might be in the flour. Be sure to let it cool completely before adding to the buttercream or it will melt the butter.
Using a standing mixer or hand held mixer with paddle attachment, cream the 2 sticks butter, salt, and ½ cup brown sugar on medium high for 2-3 minutes until very light and fluffy.
Turn the mixer off and add the powdered sugar. Mix on low until incorporated. Once incorporated turn to medium and mix another minute.
Add flour, mix on low until incorporated, then mix on medium another minute.
Add 2 tbsp milk or cream and 1 tsp vanilla extract. Mix on medium low until combined, then mix another minute on medium until light and fluffy.
Using a spatula gently fold in the chocolate.
