Peel the onions and cut in half, then slice thinly, about ¼" thick slices.
Heat the oil in a large sauté pan over medium-low heat and add the onions and the salt.
Stir so that the onions are coated in the olive oil and let cook for about 3 or 4 minutes, until the onions begin to sweat and release some liquid into the pan.
Turn the heat down to low and let the onions continue cooking, stirring occasionally, for about an hour, until they are completely softened and golden.
Allow to cool completely, then put into an airtight container and refrigerate for up to one week.