Put chicken, water, large onion chunks, cumin, thyme and bay leaf in large pot and bring to boil. Reduce heat to simmer for 45 minutes. Remove chicken, discard skin, bones, joints, tendons, etc. Shred meat. Strain broth and discard onion, thyme and bay leaf.
Return chicken, broth, garlic and hominy back into pot, season with salt & pepper and bring to simmer for 15 minutes. Bring to rolling boil before serving.
Serve very hot soup garnished with cabbage, radishes, cilantro, chopped onion, jalapeno, lime and oregano.