Using an electric mixer, beat the butter and both sugars in large bowl until well-blended. Add the egg and vanilla and beat until fluffy. Beat in the flour, salt and baking soda. Stir in the Butterfingers (the dough will be moist). Chill the cookie dough at least 30 minutes and up to 1 hour.
Preheat oven to 350°F. Line baking sheets with parchment paper. Using 1 rounded tablespoon of dough for each cookie (I use a small cookie scooper), drop the cookie dough in mounds onto the prepared baking sheets, spacing 3 inches apart (about 8 cookies per sheet; the cookies will spread). Bake the cookies until golden brown, about 12 minutes. Transfer the parchment with the cookies to a rack and cool completely.
Notes
These cookies can be prepared 4 days ahead. Store in an airtight container.