Preheat oven to 350°F with racks in upper and lower thirds. Whisk together flour, baking soda, and 1 ½ teaspoons salt. In a mixer fitted with the paddle attachment, beat butter with granulated sugar and 2 tablespoons zest on medium speed until light and fluffy, 2 to 3 minutes.

Add eggs, one at a time, beating well after each addition. Beat in 1 teaspoon vanilla. Reduce speed to low and add half of flour mixture, then buttermilk, then remaining flour mixture, scraping down sides of bowl as needed. Beat until smooth.

Line two baking sheets with parchment. Spoon ¼ cup dough into mounds on sheets, 6 per sheet. Bake, rotating sheets and rack positions halfway through, until edges are lightly golden, 15 to 18 minutes. Transfer cookies to a wire rack; let cool completely. Repeat with remaining batter.

In a bowl, whisk together confectioners' sugar, corn syrup, remaining pinch of salt and ¾ teaspoon vanilla, and 3 tablespoons juice until smooth. Transfer half of icing to another bowl; whisk in cocoa and 1 to 2 tablespoons hot water until you reach desired consistency. Add remaining ½ teaspoon zest and tint with 1 to 2 drops of food coloring. (Icing should be a bit thicker than honey; if needed, whisk in more juice.)

Flip cookies flat-sides up. Using a small offset spatula, spread grapefruit icing over half of each cookie and chocolate icing over other half. Let stand until icing is set, about 1 hour. Cookies can be stored in a single layer in an airtight container at room temperature up to 2 days.