Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, allspice, cardamom, and nutmeg. Set aside.
Using an electric mixer on medium speed, beat the butter, brown sugar, and sugar until light and fluff. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce mixer speed to low. Gradually add the flour mixture, mixing just until combined. Stir in the toffee bits.
Drop the dough by 2-tablespoon portions (a cookie scoop works well for this) onto the prepared pans. Flatten the cookies slightly. Sprinkle each with more toffee bits and a pinch of turbinado sugar if you like.
Bake 14 to 16 minutes, or until the edges are browned and the centers appear set. (Refrigerate remaining dough between batches.)
Cool on the pans for 5 minutes. Then transfer the cookies to a wire rack to cool completely.