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1
Preheat the oven to 375F.
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2
Make cookies: Sift together flour, cocoa powder, baking soda, and salt into a bowl.
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3
Put butter and sugar into the bowl of an electric mixer fitted with the paddle attachment.
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4
Mix on medium-high speed until pale and fluffy, about 2 minutes.
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5
Reduce speed to medium-low; mix in egg, milk, and vanilla.
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6
Mix in flour mixture, 1/2 cup at a time, until combined.
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7
Using a 1 3/4-inch ice cream scoop, drop dough onto baking sheets lined with parchment paper, spacing 2 inches apart.
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8
Bake cookies, rotating sheets halfway through, until firm, 8 to 10 minutes.
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9
Immediately press a marshmallow half on top of each cookie.
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10
Bake until marshmallows begin to melt, 2 minutes more.
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11
Let cool completely on sheets on wire racks.
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12
Make frosting: Put confectioners sugar in a medium bowl.
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13
Melt butter with the cocoa powder in a saucepan over medium-low heat, stirring occasionally.
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14
Add butter mixture to the confectioners sugar.
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15
Whisk in milk and vanilla.
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16
Spread about 1 tablespoon of frosting on top of each cookie to cover marshmallow.
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17
Let stand until set, about 10 minutes.
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18
Cookies can be stored in single layers in airtight containers at room temperature up to 2 days.
