Preheat oven to 350°F. Line cookie sheets with parchment paper and set aside.
Spread the 1 cup (or so) sliced almonds (for topping) in a single layer on a small baking sheet and toast in the preheated oven 5–7 minutes, watching closely, until light golden. Remove and cool completely. (Keep oven on for the cookies.)
In a medium bowl, whisk together 2-1/4 cups flour and 1 teaspoon baking soda; set aside.
In a large bowl, cream together 1 ½ sticks butter, ¾ cup brown sugar, and ¼ cup sugar until light and fluffy.
Add the 1 (3.4 oz) package instant vanilla pudding mix to the creamed butter and sugars and beat until well blended.
Add 2 eggs and 1 teaspoon almond extract to the mixture and beat until combined.
Gradually add the flour/baking soda mixture to the wet ingredients and mix just until combined (do not overmix).
Stir in 1 cup chopped sliced almonds until evenly distributed.
Roll dough into 1-inch balls and place them about 2 inches apart on the prepared cookie sheets.
Bake at 350°F for 10–12 minutes. Remove from oven and transfer cookies to a wire rack to cool completely before frosting.
To make the frosting: in a small saucepan over low heat, combine ½ cup brown sugar, 2 tablespoons milk, and 3 tablespoons butter. Stir until the brown sugar is completely dissolved into the liquid, about a few minutes. Remove from heat.
Immediately stir in ½ teaspoon almond extract, then add 1 cup powdered sugar and stir until smooth with no lumps. Work quickly—the frosting will begin to set.
Frost the cooled cookies, top each cookie immediately with the toasted sliced almonds, and allow the frosting to harden before serving.