Cream butter and brown sugar. Stir in vanilla and flour.
Cover and chill for 1 hour.
On a floured surface, roll out into a rectangle about 1/4" thick. Cut with a small cookie cutter, or just use a knife to cut rectangle shapes. I used a knife. It's fine if the cookies aren't all the exact same size. Just call them rustic. :)
Place on parchment or silpat lined cookie sheets and bake at 350° for about 12 minutes or till barely lightly browned around the edges. Cool completely on cooling racks.
Melt butter in a glass bowl in the microwave. Add the chocolate chips and cook at half power, stirring every 30 seconds till smooth and creamy.
Dip cookies halfway into the melted chocolate, then place on silicone liners or waxed paper. Sprinkle toffee bits on the melted chocolate. Let sit till chocolate is hardened.