How to mix butter with meat
+1 @megha Grating frozen (or very cold refrigerated) butter is the way to go here. It's best to add the grated butter to the mince after the meat has been ground. Grating butter is easily done in a food processor (industrial or home) - we did it all the time at an old restaurant I worked at and I still do it at home for pastry crust.

Random source: 
http://people.com/food/grated-butter-burgers-recipe-food-hack/

Alternative idea - America's Test Kitchen did a Butter Burger bit awhile back that people claim is amazing: 
https://www.youtube.com/watch?v=WAUpelESAXo