Heat the olive oil in a large skillet over medium heat. Add the remaining ingredients. Stir well to mix. Cook, stirring occasionally, for about 20 minutes until the peppers are just tender. Taste for seasonings.
Remove from the heat and transfer to the bowl of a food processor fitted with a metal blade. Cover and process for about 20 seconds until the mixture is blended—alittle chunky, but mainly blended. Serve warm or cool to room temperature then refrigerate for up to 3 days. Serve chilled or at room temperature.