A material to be extracted and an edible fat are introduced into an extractor equipped with a device for collecting stream and gases, such as a condenser. The contents are heated, and the resultant extract is cooled. The distillate collected with the condenser during heating is returned to the extractor. Alternatively, the distillate is further extracted with an edible oil and/or fat and the extract obtained by the distillate extraction with the oil and/or fat is returned to the extractor. Thus, an oil-based processed flavor with a cooked note is produced. This oil-based processed flavor with a cooked note is added to or incorporated in a food or beverage as it is or, if necessary, after having been diluted, emulsified, powdered, or otherwise treated.