Preheat oven to 350.
Line 3 cookie sheets with parchment paper; set aside.
In a medium bowl sift together the flour, baking soda, and salt; set aside.
In a small bowl, whisk together the superfine sugar and light brown sugar; set aside.
Place the butter in your mixer's bowl and beat until creamy and smooth.
Slowly add the sugar mixture; continue to beat until thoroughly combined.
Mix in the vanilla.
Continue to beat for 5 minutes, or until the mixture is a pale yellow.
Gradually beat in the eggs.
With the mixer speed on low, slowly mix in the flour mixture; continue to beat until incorporated.
Fold in the chocolate chips and toasted sliced almonds.
Scoop out the dough using a 2-inch diameter ice cream scoop, and drop batter onto the prepared pans, leaving at least 3 inches in between each cookie.
Flatten each ball of dough with the heel of your palm.
Bake for 15 to 18 minutes, or until the cookies are golden brown.
Rap each pan on the rack 3 minutes before the cookies are done baking. This will make the cookies deflate and cracks will appear on the tops.
Repeat with the rest of the cookies.
Cool cookies on the pans.