Combine soft butter, pumpkin puree, egg yolk and vanilla in a medium-size bowl. Mix until smooth and well blended.
Sprinkle flour, pumpkin pie spice, baking soda and salt over the top of the pumpkin mixture and mix until well combined. Add toffee bits (if using) and stir again.
Refrigerate dough for 15 minutes while the oven is preheating.
Using a cookie scoop or a tablespoon, drop rounded scoops of dough onto prepared sheet pans, spacing 1 1/2-2 inches apart. Bake for 10 minutes, then sprinkle 1/2-1 teaspoon toffee bits over the top of each cookie. Return to oven for another 3-5 minutes or until puffed and golden brown.
If not using toffee bits for garnish, bake cookies for 14-16 minutes, or until puffed and golden brown. Allow cookies to cool (they will firm up) for several minutes before transferring from pan to a cooling rack. Cool complete then store in an airtight container.