Preheat the broiler oven (500°F or 260°C) and position an oven rack on the top shelf or as close as possible to the broiling element.
To start the sauce, return to the chiles, and once they have softened, pour off 1 cup of the soaking liquid and reserve for sauce. Next, add the chiles to a blender.
Broil the vegetables on a sheet pan lined with aluminum foil (for easy clean-up). Core and slice the tomatoes in half and add the garlic clove (still in the paper tunic). Drizzle a little oil on the tomatoes. Cook under the broiler until charred, about 7-10 minutes. After the tomato and garlic are cooked, lower the oven to Bake at 350°F or 175°C).
Peel the garlic cloves and tomato and add to the blender with the reconstituted chiles. Add the toasted sesame seeds, chocolate, ground clove, and cinnamon. Add the reserved chile soaking liquid and the chicken stock. Process the mixture in a blender.
Once the mole mixture is smooth, strain the sauce through a fine mesh strainer over a mixing bowl. Reserve.
Heat the lard or vegetable oil in a large skillet until hot or shimmering over medium-high heat. Slowly add the strained mole sauce, which will instantly start to sizzle. Continue adding until it is all in the pan, and keep heating until it cooks thoroughly. Reduce the heat and partially cover with a lid. Simmer for 1 hour, stirring often.