Combine figs and mezcal in a glass container with a tight-fitting lid. Seal and leave at room temperature to infuse for 1 week.
Pour into a blender, blend until figs are completely puréed. Strain through a fine mesh strainer into a large measuring cup. Press on the solids to extract all mezcal. You should have about 1 cup of Fig-Infused Mezcal.
Use right away or keep in a tightly-sealed container for up to a month at room temperature.
Combine all the ingredients for the ginger syrup in a small saucepan. Bring to a simmer over medium heat. Whisk to dissolve the sugar and simmer for 5 minutes. Remove from heat and steep until cool. Strain out the ginger.
Use right away or keep in a tightly-sealed container in the refrigerator for up to 2 months.
Rub a lime or orange wedge on the rim of a cocktail glass. Dip in coarse salt and fill glass with ice.
Fill a cocktail shaker with ice. Add Fig-Infused Mezcal, Ginger Syrup, and lime juice. Shake vigorously. Strain into prepared glass. Garnish with a California Dried fig, an orange wedge and a lime wedge. ¡Salúd!