Dice the onions, carrots and celery as evenly as possible - the finer the dice, the more smoothly the soffritto will blend into sauces and soups later.
In a large skillet or saucepan, heat the olive oil over medium heat.
Add the onions first and cook until translucent, then stir in the carrots and celery. Cook gently for 15-20 minutes, stirring occasionally, until everything has softened and melded together. Avoid letting the vegetables brown.
Let the soffritto cool completely, then divide it into portions of about 1/4 cup each for storing.