Cut the green tops off all the peppers. Discard tops and set peppers aside.
Slightly smash each clove of garlic just enough that the paper loosens; remove the paper and discard it.
In a medium, non-reactive (i.e. stainless steel, ceramic, or glass) pot, add the prepared peppers and garlic cloves. Pour in the vinegar and lime juice then add the salt, paprika, and bay leaf. Stir together to mix in the salt and paprika.
Bring the mixture to a boil. Reduce heat to medium-low, cover, and allow to simmer for 20 to 30 minutes or until the peppers are soft.
Remove from the heat and add to a food processor or heat safe blender (no need to remove bay leaf). Pulse until smooth and liquidy (be CAREFUL--it is HOT), adding more vinegar if necessary to make it more liquid.
Smoosh through a fine mesh sieve into a bowl and discard any seeds and large chunks left in the sieve.
Refrigerate in an airtight container for at least one week prior to using.
This recipe lasts about 6 months in the refrigerator (if it smells funky or it's growing something, discard).
It can also be canned. Follow the proper and safe canning procedures as recommended by your state, province, or country.