Rinse well in a colander; let drain.
In a 5 quart Dutch oven, cook bacon until crisp; set aside to drain on paper towels.
Cook onion and celery in bacon drippings until tender.
Add garlic the last minute or two.
Drain excess grease.
Add broth, sugar, salt, pepper and peas.
Bring to a boil and skim top to remove foam or scum if necessary.
Lower heat to a simmer; crumble bacon and add to peas.
Cover and simmer until peas are tender, 45 minutes to 1 1/2 hours, depending on how you like your peas cooked.
Check water level occasionally, making sure the peas have just enough to cover them.
When done, taste and adjust seasoning.
If using fresh or frozen peas, cooking time will be less, 30 minutes to 1 hour.