Put the chicken into a saucepan with the garlic, onions, and mint. Add the water to cover and salt to taste. Bring to a simmer, cover the pan, and continue simmering until the chicken is just tender, about 35 minutes. Strain, reserving the broth. Remove the stems from the dried chiles. Slit them open, and remove seeds and veins, reserving the seeds. Toast the chiles for about 50 seconds on each side; if you're using guajillos, toast them longer, until they are almost charred, about 2 minutes.
Rinse the chiles in cold water, cover with hot water, and leave to soak for about 30 minutes. Put the reserved chile seeds into an ungreased frying pan and toast over fairly high heat, shaking them around from time to time so that they brown evenly. Then raise the heat and char until black. Cover with cold water and set aside to soak for about 5 minutes. Strain and put into a blender jar. Add the broiled tomatoes, unpeeled, to the blender jar along with the water, cloves, allspice, thyme, marjoram, and oregano.
Heat some of the lard in a small frying pan and fry the sesame seeds until a deep golden color, a few seconds. Strain, putting the fat back into the pan and the seeds into the blender jar, and blend as smooth as possible. Fry the rest of the ingredients, except the chiles and chocolate, 1 by 1, strain, and put into the blender jar, blending after each addition and adding water or broth, as necessary, to release the blades.
Heat 1/4 cup of the lard in the heavy pan in which you are going to cook the mole, add the blended mixture, and fry over medium heat, stirring and scraping the bottom of the pan from time to time, for about 15 minutes. Meanwhile, put a few of the chiles and about 2 cups of the water in which they were soaking into the blender jar and blend until smooth. When you have blended all the chiles, add them to the fried ingredients together with the chocolate and cook for 5 minutes longer.
Add about 4 cups of the chicken broth and continue cooking for 35 minutes. Skim the fat that forms on the top if you are going to make tamales or mole. It is added to color and flavor the masa. Add more broth if necessary, the mole should just coat the back of a wooden spoon. Add the chicken and salt to taste; cook for 10 minutes longer.