Put the oil and chopped garlic in a soup pot and turn on the heat to medium. Cook the garlic, stirring it, until is becomes colored a very pale gold.
Add the drained cooked or canned beans, a pinch of salt, and a few grindings of pepper. Cover and simmer gently for 5 to 6 minutes.
Take about 1/2 cup of beans from the pot and puree them through a food mill back into the pot, together with all the broth. Alternately, use a blender, loosening with a bit of the broth. Simmer for another 5 to 6 minutes, taste, and correct for salt and pepper. Swirl in the chopped parsley, and turn off the heat.
Ladle over the grilled bread slices into individual soup bowls.
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