Beat butter, sugar, extract and salt in large mixer bowl until creamy. Beat in flour; half cup at a time until well blended. Stir in toffee bits and peanuts.
Take a tablespoon of dough and shape into ball; continue until all the dough is used. Place on ungreased cookie sheets.
Bake 10 to 12 minutes are until lightly browned. Remove from oven and sift powdered sugar over the top while still hot. Cool on baking sheets at least 10 minutes; then carefully put them to wire racks to cool completely. This cookie is very fragile while warm.
Store in airtight containers; can be frozen and used later.