Heat oil in a medium nonstick skillet over medium heat. Add onion and 1/4 teaspoon salt, and cook 22 minutes or until golden brown, stirring frequently. Add 2 tablespoons water, 1 tablespoon at a time, as liquid evaporates, scraping pan to loosen browned bits after each addition. Remove from heat, and set aside.
. While onion cooks, place potato in a Dutch oven, and add water to cover. Bring to a boil; reduce heat, and simmer, uncovered, 15 minutes or until tender. Drain and return to pan.
. Place milk in a 1-cup glass measure. Microwave at MEDIUM (50% power) 30 seconds or until warm.
. Add cheese to potato in pan. Mash potato mixture with a potato masher 3 or 4 times or until cheese melts. Add milk, remaining 1/2 teaspoon salt, and pepper; mash to desired consistency. Stir in reserved onion, and serve immediately.