Preheat your oven to 350°F (175°C). Line a large baking sheet with parchment paper or a silicone baking mat to prevent sticking and make cleanup easier. Set the prepared sheet aside until you’re ready to bake.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt until well combined. This helps distribute the leavening agents and salt evenly throughout the flour.
In the bowl of a stand mixer fitted with the beater blade, beat the softened unsalted butter, white sugar, and packed brown sugar together for about two minutes until light and fluffy. Add the almond paste in small pieces and continue mixing until fully incorporated. Then add the eggs one at a time, mixing well after each addition. Finally, mix in the vanilla extract until everything is thoroughly blended. I like to scrape down the sides of the bowl occasionally to ensure everything mixes evenly.
Gradually add the dry ingredients from Step 2 to the wet mixture from Step 3, mixing slowly just until the flour is incorporated and no visible streaks remain. Be careful not to overmix, as this can make the cookies tough. Gently stir in the chopped toffee pieces and semi-sweet chocolate chips by hand until evenly distributed throughout the dough.
Using a medium cookie scoop, drop portions of dough onto the prepared baking sheet from Step 1, spacing them about 2 inches apart. Bake the cookies in the preheated oven for 12–14 minutes, or until they are golden brown around the edges. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely. For extra-dimensional flavor, I sometimes sprinkle a touch of flaky sea salt on top while the cookies are still warm.