Make the mole-infused tequila: In a spice grinder or coffee mill, finely grind the ancho, guajillo and cascabel chiles. Add the ground chiles, cinnamon stick, cloves and cumin to the tequila, cap and let sit for 36 hours. Strain through a coffee filter and return to the bottle.
Make the mole lime wedge: Mix the cayenne, cocoa powder, cumin, cinnamon and cloves on a plate and dredge one side of the lime wedge in the mixture. Set aside.
Fill a cocktail shaker with ice and add 1½ ounces of the infused tequila, the mezcal, lime juice, grapefruit juice, Chartreuse, Fernet Branca and bitters. Cover and shake well. Strain into a coupe glass, garnish with the prepared lime wedge and the thyme sprigs and serve.