Preheat the oven to 350°F (175°C). Place a rack in the center of the oven. Line a large baking sheet with parchment paper or a silicone baking mat and set aside.
In a medium bowl, whisk together the 2 3/4 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon salt until evenly combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup unsalted butter (at room temperature), 3/4 cup granulated sugar, and 3/4 cup brown sugar on medium speed for about 2 minutes, until light and creamy. Stop once or twice to scrape down the sides of the bowl.
Break the 3 ounces almond paste into small pieces and add them to the butter-sugar mixture. Mix on medium speed until the almond paste is fully incorporated and the mixture is smooth.
Add the 2 large eggs one at a time, mixing on low speed after each addition until just combined. Add 1 1/2 teaspoons vanilla extract and mix until blended.
With the mixer on low speed, add the dry ingredients to the wet ingredients in two additions, mixing just until no streaks of flour remain. Do not overmix.
Transfer the dough to a large bowl (or keep in the mixer bowl) and fold in 1 1/2 cups chopped toffee and 1 cup semi-sweet chocolate chips with a spatula until evenly distributed.
Using a medium cookie scoop, portion the dough onto the prepared baking sheet, spacing the mounds about 2 inches apart.
Bake one sheet at a time on the center rack for 12–14 minutes, until the cookies are golden brown around the edges and set in the centers.
Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes, then transfer the cookies to a cooling rack to cool completely.