Line two baking sheets with parchment paper, and set aside.
Place the butter in a medium saucepan, and turn the heat to Medium-Low. Use a wooden spatula or spoon to stir the butter as it melts. Continue stirring as the butter cooks and turns brown–you'll know it's ready when the butter has turned foamy, there are small brown bits in the melted butter, and the melted butter has a nutty aroma. This will take about 5-7 minutes. The butter can turn from browned to burned very quickly, so remove the butter from heat once is brown in color and you see those brown bits on the bottom. Allow the butter to cool slightly before transferring to a large bowl, or the bowl of a stand mixer. Add the brown sugar and white sugar, and beat for about 1-2 minutes until combined. The mixture will not be completely smooth and incorporated–that’s ok.
Add the egg and vanilla extract, and beat again for another minute until the batter is fluffy, creamy, and light in color.
Pour in the flour, salt, and baking soda, and use a spatula or spoon to lightly fold the dry ingredients into the batter until few dry streaks remain. Be careful not to overmix it.
Add in the graham cracker crumbs, toffee buts, and chocolate chips. Fold those into the batter until no dry streaks remain.
Scoop the cookie dough onto one of the baking sheets (it’s ok if the dough balls are touching). Cover with plastic wrap and refrigerate for 1 hour.
When ready to bake, preheat oven to 350 F.
Place 6 cookie dough balls on the second baking sheet, spaced about 2” apart as the cookies will spread.
Bake for 13-15 minutes, until the cookies are golden brown on the edges.
Repeat with the remaining cookie dough balls–or, place those dough balls in an airtight container and freeze for longer storage.
Bake from frozen: Place frozen cookie dough balls on a baking sheet lined with parchment paper, and bake in a 350 F oven for 15-20 minutes when ready to enjoy!