Using tongs, char jalapeño on stovetop on an open flame over high heat, turning until blackened, about 3 minutes total. Alternatively, heat a small pan over high heat and char jalapeño all over. Remove to a work surface and let cool slightly. When cool enough to handle, thinly slice the jalapeño.
Then, pour a mound of salt onto a small plate and spread out slightly. Rub a lime wedge around the rims of two rocks or margarita glasses. Dip rims into salt and turn to coat. Fill glasses with ice.
Combine tequila, carrot juice, triple sec, lime juice, and 4 slices of jalapeño in a cocktail shaker. Fill shaker with ice, cover, and shake vigorously until very cold. Strain into the prepared glasses and garnish each with a baby carrot, a piece of lime, and a few slices of charred jalapeño. Serve immediately.