Heat the oven to 350°F. Cover a cookie sheet with parchment paper to keep the cookies from sticking and to make cleanup easier.
Place the unsalted butter, brown sugar, and granulated sugar in the bowl of a stand mixer. Alternatively, use a large mixing bowl with an electric hand mixer.
Beat the mixture for 3–4 minutes, or until it becomes pale, light, and fluffy. Scrape down the sides and bottom of the bowl as necessary so the ingredients blend evenly.
Add the room-temperature egg and vanilla extract to the creamed butter mixture.
Continue mixing until the egg and vanilla are completely incorporated and the mixture has a smooth, even consistency.
In a separate small bowl, whisk the all-purpose flour, baking powder, and baking soda together until evenly combined.
Add the flour mixture to the wet ingredients and mix only until a cohesive cookie dough forms. Avoid excessive mixing.
Add the Heath toffee pieces to the dough and gently fold them in until they are distributed evenly throughout the mixture.
Scoop approximately 2 tablespoons of cookie dough for each cookie and arrange the portions on the parchment-lined baking sheet. Continue until all of the dough has been portioned.
Place the baking sheet on the center rack of the preheated oven. Bake for 10–12 minutes, or until the cookie edges develop a golden-brown color.
Remove the baked cookies from the oven and leave them on the baking sheet for 2–3 minutes.
Transfer the cookies to a wire cooling rack and allow them to cool completely before serving.