Sift flours, baking soda, baking powder and salt into a bowl. Set aside.
Using a stand mixer with the paddle attachment (or a hand held mixer) cream butter and sugars together until very light, about 5 minutes.
Add eggs, one at a time, mixing well after each addition. Add in the vanilla.
Reduce speed to low, add dry ingredients and mix until just combined, 5 to 10 seconds.
Add in the chocolate pieces (and toffee if adding) and gently incorporate to prevent breaking them.
Scoop 3 1/2-ounce mounds of dough (the size of generous golf balls) onto a baking sheet.
Cover the dough by pressing plastic wrap against the surface of the dough and refrigerate 24 to 36 hours. Dough can be refrigerated for up to 72 hours or frozen at this stage.
When ready to bake, preheat oven to 350 degrees.
Line a baking sheet with parchment paper or a nonstick baking mat. Set aside.
Sprinkle lightly with sea salt and bake until golden brown but still soft, 18 to 20 minutes.
Transfer sheet to a wire rack for 10 minutes, then slip cookies onto another rack to cool a bit more. Repeat with remaining dough, or reserve dough.