Prepare the graham crumbs: Pulse graham crackers in a food processor or crush in a zip-top bag until finely ground.
Mix dry ingredients: In a medium bowl, combine flour, graham crumbs, baking soda, and salt. Set aside.
Cream butter and sugars: In a large mixing bowl, beat softened butter with brown and granulated sugar until light and fluffy, about 2 minutes.
Add wet ingredients: Mix in egg and vanilla extract until fully incorporated.
Combine: Gradually add the dry mixture to the wet ingredients, stirring just until combined.
Fold in mix-ins: Add toffee bits, chocolate chips, and nuts (if using). Mix gently to distribute evenly.
Chill: Cover the dough and refrigerate for 30 minutes to help prevent spreading.
Preheat oven: Set to 350°F (175°C) and line two baking sheets with parchment paper.
Scoop and shape: Use a cookie scoop to portion dough (about 1½ tablespoons each) and place 2 inches apart on the baking sheet.
Bake: Bake for 9–11 minutes, until edges are golden but centers are still soft.
Cool: Allow cookies to cool on the sheet for 5 minutes before transferring to a wire rack.