In a food processor or blender, combine the fresh cilantro leaves, garlic, olive oil, lime juice, salt, and black pepper.
Blend the ingredients until they begin to break down, scraping down the sides of the processor or blender as needed to ensure everything is well combined.
With the motor running, gradually add water, a little at a time, until the sauce reaches your desired consistency. You may not need to use all of the water.
Continue blending until the cilantro sauce is smooth and vibrant, with a pourable yet slightly thick texture.
Taste the sauce and adjust the seasoning, adding more salt or lime juice if desired.
Transfer the cilantro sauce to a jar or airtight container, and refrigerate for at least 30 minutes before serving to allow the flavors to meld together.