Make the cookies: Preheat oven to 350 degrees and line a baking sheet with parchment paper.

In a medium bowl, whisk together flour, baking soda, and salt. 

In the bowl of a stand mixer fitted with a paddle attachment or working with electric beaters and a large bowl, beat butter and sugar on medium-high speed until light and creamy, 4 to 5 minutes.

Add egg and beat until just blended. Scrape down the sides of the bowl and add the buttermilk and vanilla, beating until smooth. 

Reduce speed to low and gradually beat in the flour mixture just until no dry streaks remain.

Use a 2-ounce ice cream scoop to place scoops onto prepared baking sheet about 3 inches apart. Bake about 15 minutes, until golden and springy to the touch.

Cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Make the icing: In a double boiler or a medium heatproof bowl set over a pot of water, combine sugar, water, corn syrup, and cream of tartar. Bring the water in the pot to a soft boil over medium heat, then lower heat to a simmer and whisk the sugar mixture constantly until the mixture thickens, about 15 minutes. Remove from heat and stir in the vanilla. Divide between two bowls and add chocolate chips to one bowl while fondant is still hot. Mix in the chips to combine, adding more hot water as needed to achieve a spreadable consistency.

Spread vanilla icing on half of the flat side of each cookie, then frost the other halves with chocolate icing. Add hot water to the bowls of the icing by the ½ teaspoon to maintain a spreadable consistency. Let set for 30 minutes before serving.