Combine softened butter and sugars with a handheld or stand mixer on medium-high until fully incorporated and starting to fluff.
Add egg and vanilla. Beat on high until pale and very fluffy (about 1-2 minutes).
Add all dry ingredients. Mix on low until thoroughly combined.
Once toffee is room temperature is room temperature and solid, set in freezer for 5-7 minutes.
Preheat oven to 350F.
Remove toffee from freezer and cut into ~1/2” squares using a large sharp knife. (Don’t be foolish like me when I first started using a silicon baking mat – put the toffee on a cutting board first so you don’t ruin your mat.)
Add all toffee pieces to cookie dough and fold in. Set in fridge for 5 minutes until oven has finished pre-heating. (Just because you don’t have to chill it for an hour doesn’t mean a little chill doesn’t help the texture.)
Hand form dough into balls of about 1 heaping tablespoon. Place on baking sheets lined with silicon mats or parchment paper. Cookies will spread 2-3” in diameter.
Bake for 13-15 minutes until cookies are barely golden on the edges. If you bake multiple sheets at a time, place the oven racks close together in the center of the oven and rotate sheet positions at about 8 minutes in.
Remove from oven and allow cookies to cool at least 3 minutes before removing from sheets.
Repeat baking with rest of dough. Cookies can be eaten immediately, in which case they are very chewy and soft, or allowed to cool and stored in an airtight container (unless you are a very odd person, they will be eaten before you can even think of them going bad). The cookies get crunchier when allowed to cool, but are not especially crisp. Can also be frozen for later consumption.