Cut 1 head of garlic crosswise in half.
Place in large pot with ribs, 3 quarts water and quartered onion.
Bring to boil over high heat.
Reduce heat to medium and simmer uncovered until meat is cooked through, about 50 minutes.
Strain, reserving 6 cups meat broth.
Discard onion and garlic.
Preheat oven to 400°.
Wrap remaining head of garlic tightly in foil and place directly on oven rack.
Place tomatoes and sliced onion on rimmed baking sheet.
Drizzle with 1 tablespoon oil.
Sprinkle with salt and pepper.
Roast garlic, tomatoes and onion until tender, for about 1 hour.
Transfer tomatoes and onion to processor.
Using fingers, squeeze garlic from papery skin into processor.
Blend until smooth.
Set tomato sauce aside place quajillo and ancho chilies in medium bowl.
Add 4 cups reserved meat broth.
Let stand for 30 minutes.
Transfer mixture to processor and blend until smooth.
Strain chili sauce into medium blend until smooth.
Strain chili sauce into medium bowl, pressing on solids in strainer with rubber spatula to exct as much liquid as possible.
Heat remaining 2 tablespoons oil in heavy large pot over medium-high heat.
Add chili ace; simmer for 5 minutes.
Add tomato sauce, cumin, oregano and cloves.
Simmer for 5 minutes.
Add ribs, vinegar and remaining 2 cups meat broth.
Bring to simmer.
Reduce heat to low and simmer uncovered until sauce is thick for about 50 minutes.