Adjust the oven rack to the uppermost position and heat the broiler to high. Place the tomatillos on an aluminum-foil-lined rimmed baking sheet and broil until they begin to darken, about 2 minutes. Use tongs to turn tomatillos over and char their other sides, 1 to 2 minutes longer.
In a cocktail shaker, add the charred tomatillos (and any juices), ½ of a jalapeño, ½ of a serrano, the cilantro, salt, the lemon wedge and 1 lime wedge (save the other halves of the chiles for another use). Use a muddler to crush the chile mixture until everything is well combined. Add the vodka, tequila, 1 ounce water and ice. Cover and shake well, then strain into an ice-filled Collins glass. Garnish with the remaining lime wedge.