In a large bowl, beat butter with sugar until fluffy; beat in milk, egg & vanilla.
In another bowl, sift flour, cocoa powder, baking powder & salt; stir into butter mixture in 2 additions. Stir in toffee bits & nuts.
Divide dough in half; place each half on a piece of plastic wrap, roll into log about 12-13-inches long. Refrigerate, re-rolling 2 or 3 times to keep round shape if necessary during the chilling time of 4 hours.
Let stand at room temperature just long enough so you can slice them without the dough cracking or changing shape. Preheat oven to 350 F. Line a baking sheet with parchment paper. With a sharp knife, slice into 1/4-inch thick slices; place on baking sheet & bake about 8-10 minutes. Immediately transfer cookies WITH parchment to cooling rack.