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TO MAKE THE COOKIES: Preheat the oven to 350F.
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Lightly grease 2 baking sheets with cooking spray or butter, or line with parchment paper or silicone liners.
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Using an electric mixer fitted with the paddle attachment, beat the butter and the 1 cup sugar on medium-high speed until light and fluffy, about 2 minutes.
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Beat in the almond extract and salt.
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Add the flour and beat on low speed just until thoroughly combined.
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Using your hands, roll the dough into 1-inch balls.
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Put the 1/2 cup sugar in a shallow bowl and roll each cookie in the sugar to coat, if you like.
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Place the cookies about 1/2 inch apart on the prepared baking sheet and flatten by lightly pressing down on the dough with the bottom of a juice glass.
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(The cookies should be about 1/4 inch thick.)
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Bake until the bottoms begin to turn golden brown, 10 to 12 minutes.
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Dont let the tops brown or the cookies will be overdone.
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Transfer to a wire cooling rack and frost while the cookies are slightly warm.
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TO MAKE THE BUTTER FROSTING: In the bowl of an electric mixer fitted with the paddle attachment, beat the 1/3 cup butter, vanilla, salt, and warm milk on low speed until combined.
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Add the powdered sugar and beat on medium speed until combined.
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If the icing seems too runny to spread, add a few tablespoons more of powdered sugar.
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If it seems too thick, add more milk, 1 teaspoon at a time, until it reaches the desired consistency.
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Like most cookies, these are at their very best eaten the day they are baked.
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You can make the dough and stow it in a container in the refrigerator up to 1 week before baking.
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Make the icing and bake the cookies the day of your party.
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Some people dislike the taste of almond extract, but I have found that even avowed almond extract haters love these cookies without detecting their almond flavor.
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The extract lends a subtle depth of flavor, not a pronounced almond taste.
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Make the cookies once with the extract and see if the naysayers react.
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If they doId be surprisedyoull have more cookies for yourself.
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Next time you make them, you can substitute vanilla extract for the almond.
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Using a 1-inch-diameter metal ice cream scoop eliminates the drudgery from portioning out cookie dough, and insures that your cookies will be of uniform size and bake at the same rate.
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The best scoops are lever-activated and push the dough out and onto baking sheets quickly and easily.
