Preheat oven to 350 degrees.
In a medium bowl, whisk together flour, baking soda, and salt. In the bowl of a stand mixer or in a large bowl with a hand mixer, beat together butter and brown sugar. Add peanut butter and egg to mixture and beat until smooth.
Slowly add flour mixture and mix until just combined, taking care not to over-mix. Fold in toffee bits.
Drop about 1 ½ Tbsps of cookie dough onto baking sheets (I like to use a cookie scoop), placing dough about 2 inches apart. Bake for 20 minutes until cookies are just turning golden.
Let cookies cool on the pan for a couple minutes before moving to wire racks to cool completely.