Place the chiles in a small saucepan, cover with water, and bring to a boil over high heat. Cook for 5 minutes, until somewhat softened; drain and set aside.
In a nonstick or well-seasoned omelet pan or skillet, heat 2 tablespoons of the lard to rippling over medium-high heat. Add the garlic and about three quarters of the sliced onion. Cook, stirring occasionally, for 5 minutes, until the onion is wilted and just starting to color. Scrape out into a blender with the drained chiles, beans, and 3 cups of the chicken stock, process to a purée about the consistency of a thin cream soup. Add a little more stock if necessary (the beans will absorb a bit more or less depending on their age and degree of dryness). You should have about 5 cups of the mixture.
Pour the bean mixture into a medium-sized saucepan and bring to a boil over fairly high heat; reduce the heat and cook for 5 minutes, stirring occasionally.
Lightly beat the eggs with the salt. In a medium-sized skillet (you can use the same one), heat the remaining lard to rippling over medium-high heat. Add the remaining sliced onion and cook, stirring, for about 3 minutes. Add the beaten eggs and cook, stirring, until barely set, about 3 minutes (or until done to your taste). Serve in bowls with about 1 generous cup of the bean purée ladled over each portion of egg.