Preheat oven to 350 degrees F. Line two rimmed baking sheets with parchment paper.
In a medium bowl, stir together flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer, beat butter and sugar on medium-high until creamy. Beat in vanilla extract and egg until well combined.
Alternate adding in the flour mixture and buttermilk, dividing each into three additions. Mix until just combined after each addition.
Spoon tablespoonfuls of the mixture onto baking sheets, spacing them about 1-inch apart. Bake for 6 to 8 minutes, until the puffy and the centers are springy. Cool cookies completely on wire racks before frosting.
As the cookies cool, make the two icings. In a large bowl, whisk together sugar, corn syrup, lemon juice, vanilla, and water until combined. Take out half of the mixture and place in a separate bowl. Add espresso powder and cocoa powder to one of the bowls, whisking until combined. The chocolate frosting might thicken up on you, so add 1 tsp of water at a time until thinned to the same consistency as the white icing.
Both icings should be thin but not runny. Spread vanilla icing on half of each cookie, then spread with chocolate icing on the other half. Let set at room temperature for a few minutes before serving.
Store in an airtight container for about 2 to 3 days.