Brown the butter first. Add the butter to a small saucepan over medium-low heat and let it melt, stirring constantly. Continue cooking until it foams, smells nutty, and you see golden brown bits forming on the bottom of the pan. Immediately remove it from the heat and transfer to a bowl to cool.

While the butter cools, prepare the dry ingredients. In a large bowl, whisk together the flour, baking soda, and salt until evenly combined, then set aside.

In a separate large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the cooled brown butter with the brown sugar and granulated sugar for about 3 minutes, until smooth and slightly fluffy. Add the egg, egg yolks, and vanilla extract, and continue mixing for about 1 minute, until fully incorporated.

Add half of the dry ingredients to the wet mixture and mix on low speed until just combined. Add the remaining dry ingredients and mix again until a thick dough forms, being careful not to overmix—especially if using regular all-purpose flour.

Fold in the chocolate chips and toffee bits until evenly distributed throughout the dough.

Line two baking sheets with parchment paper. Use a large cookie scoop (about 3 tablespoons) to portion the dough into balls, placing them about 3 inches apart on the prepared baking sheets.

If using, gently press a teddy graham onto the top of each cookie. Bake on the middle rack for 10–12 minutes, until the edges are lightly golden and the centers are still soft.

Remove from the oven, let the cookies cool on the baking sheet for a few minutes, then transfer to a wire rack to cool slightly before enjoying.