Peel the onions, trim off their root ends, and cut them in half lengthwise. Remove the outmost layer if it looks tough or papery. Slice them lengthwise into thin strips.
Warm a good pour of olive oil in a Dutch oven or terracotta casserole, the add the sliced onions and a pinch of salt. Let the onions sauté over moderate heat for about 5 minutes or so, until they have wilted and turned translucent. They should have reduced in volume by almost half.
Pour in the water and bring the pot to a simmer. Cover and turn down the heat to low. Let the onions simmer, covered, for 30-45 minutes, or until they are very soft and translucent. Add water from time to time if the onions seems to be drying out.
Sprinkle on the red pepper flakes, as much as you care for. Let everything simmer for a few more minutes, uncovered, before serving.
The dish should be served quite wet, but not quite a soup. Add more liquid if it looks too dry and, conversely, raise the heat boil off any excess liquid.
Garnish if you like with black olives and/or a good grating of pecorino cheese, with grilled or toasted bread on the side.