2 oz. gin
Now that you're acquainted, I bet you're wondering about the name. A Cobbler cocktail uses a base of wine, sugar, fresh fruit, and ice. The original was the Sherry Cobbler, which was most popular in the late 19th century. (Your silver cocktail shaker with a built-in strainer at home? That's called a Cobbler shaker, but then you probably knew that.) The vermouth is the wine in this case, although I'm guessing it's used in a very small quantity. I tried going back to Blueprint this Friday to bribe the barkeep for the recipe, but they were closed for an event.
Curses! I'll try again soon and will share the bounty.