In a medium bowl, whisk together the flour, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, peanut butter, granulated sugar, and brown sugar until light and fluffy, about 2 minutes. Beat in the egg and vanilla. Add the dry ingredients and beat at low speed, scraping the side of the bowl occasionally, until smooth. Transfer the dough to the refrigerator and chill 15 minutes.
Preheat the oven to 350°F. Line 2 cookie sheets with parchment paper.
Roll a heaping tablespoon of dough into a 1½-inch ball and place it on the prepared baking sheet. Repeat with the remaining dough, spacing the balls about 2 inches apart. Using your thumb, dowel or a melon baller, make an indentation in the center of each cookie. Bake for 7 to 9 minutes, or until very lightly browned. Remove the cookie sheets from the oven. Using your thumb, dowel or a melon baller, press into the cookies again and place 3 or 4 mini marshmallows on top of each cookie. Return the cookies to the oven and bake 2 to 3 minutes longer, until the marshmallows are melted. Cool cookies for 5 minutes on baking sheet, then transfer to wire rack to cool completely.
To make chocolate glaze: place chocolate chips, butter and corn syrup in a medium heatproof bowl. Set bowl over saucepan containing barely simmering water; heat mixture until chocolate is melted and whisk until smooth. Add vanilla. Drizzle a small amount of chocolate glaze over the top of each cookie. Glaze will set slightly upon cooling.