Cut the butter into chunks and put in a large bowl; add granulated and brown sugars. Beat with a mixer to blend, then beat on high speed until the mixture is fluffy.
Add eggs and vanilla; beat to blend.
Add flour, baking powder, baking soda, and salt. Mix on slow speed to incorporate dry ingredients, then beat on medium speed until well blended.
Stir in almond brickle.
Drop cookie dough in rounded teaspoon portions about 2 inches apart on oiled or nonstick baking sheets.
Bake in a 375° oven until golden brown, 8 to 10 minutes (if using one oven, alternate pan positions after 4 to 5 minutes).
Cool about 2 minutes on pan. With a wide spatula, transfer cookies to racks to cool.
Serve, or store airtight at once for up to 3 days. Freeze to store longer.
Nutritional analysis per cookie.