Marshmallow is the star ingredient in these chewy-sweet sandwich cookies. Lightly toasting a tray of marshmallows deepens their toasty vanilla-sugar flavor and softens them just enough to beat with butter to create the base of the smooth, slightly sticky batter. After baking, gooey marshmallow creme is sandwiched between them for a final pop of marshmallow texture.
Preheat the broiler. Line a baking sheet with foil and lightly coat with cooking spray. Spread the marshmallows on the baking sheet and broil until puffed and toasted (but not charred), flipping halfway through, 1 1/2 to 2 minutes. Set aside to cool.
Meanwhile, whisk the flour, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Add the egg and vanilla and beat until smooth, about 1 minute, scraping down the bowl as needed. Add the cooled toasted marshmallows and stir with a rubber spatula, smashing in the marshmallows until incorporated (a few marshmallow lumps are fine). Add the flour mixture and stir until just combined. Cover the dough and refrigerate until no longer sticky, 2 to 4 hours.
Position racks in the upper and lower thirds of the oven and preheat to 350˚ F. Line 2 baking sheets with parchment paper. Spread the sanding sugar in a shallow bowl. Scoop the chilled dough into 24 balls, about 1 1/2 tablespoons each. Roll in the sugar and arrange about 2 inches apart on the baking sheets. Bake, switching the pans halfway through, until the cookies are set and lightly golden around the edges, 10 to 15 minutes. Let cool 3 to 5 minutes on the pans, then remove to a rack to cool completely.
Turn half the cookies over so the flat side is up. Top each with about 2 teaspoons marshmallow cream. Let stand about 5 minutes so the marshmallow starts to spread, then top with a second cookie, flat-side down. Gently press and let stand about 10 minutes more; the marshmallow cream will spread to the edge.