In a large mixing bowl or the bowl of a stand mixer, cream butter and confectioners sugar together until completely smooth. Mix in the vanilla.
On low speed, add the flour and mix until combined and a dough is formed. Fold in the chocolate chips and toffee bits using a wooden spoon or spatula.
Divide the dough into half and shape each half into a log that is 12" long and about 1½" wide. Wrap the logs in plastic wrap and refrigerate for at least 2 hours to firm or up to 3 days.
Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
Slice the cookie logs into ¼"~½" slices. Place them on the prepared baking sheet and bake for 12~15 minutes or until the edges are firm to touch and just lightly brown. Rotate the pans once in the middle for even baking.
Let the cookies cool on the baking sheet completely before removing from the pan.