Heat the oven to 350°F. Make certain the butter has softened to room temperature and the eggs are no longer cold, as this encourages smoother blending and better emulsification.
Sift the all-purpose flour and baking soda together in a medium mixing bowl. This aerates the flour while distributing the baking soda evenly. Set the mixture aside and measure the remaining ingredients before proceeding.
Place the softened salted butter, granulated sugar, and firmly packed light brown sugar in a large mixing bowl. Beat for 2–3 minutes, or until the mixture becomes noticeably paler, fluffier, and greater in volume.
During the final minute of creaming, pour in the vanilla extract and continue beating until it is thoroughly incorporated.
Add the room-temperature eggs individually, beating thoroughly after each addition before adding the next.
Once both eggs have been completely blended into the butter mixture, gently fold in the toffee bits until evenly dispersed throughout the dough.
If desired, retain a small handful of the toffee pieces to scatter over the portioned cookies immediately before baking.
Add the prepared flour mixture to the wet ingredients in two or three portions. Stir gently after each addition, mixing only until the flour has been incorporated.
Avoid excessive mixing after the flour is introduced, since unnecessary agitation can develop the gluten and produce a firmer cookie. Stop as soon as no visible streaks of dry flour remain and the dough has formed a cohesive mixture.
Using a cookie scoop or spoon, divide the dough onto an ungreased or parchment-lined baking sheet. Leave approximately 2 inches of space between portions to accommodate spreading.
For improved structure and a chewier center, refrigerate the portioned or prepared dough for 30–60 minutes before baking. The cookies may also be baked immediately when time is limited.
Bake at 350°F for 10–12 minutes. Remove the cookies when the edges have developed a golden-brown color while the centers still look slightly underbaked. Residual heat from the baking sheet will continue cooking the centers after they leave the oven.
Allow the cookies to remain on the baking sheet for 3–5 minutes so they can firm sufficiently. Transfer them carefully to a wire rack and leave them there until completely cooled.