Preheat oven to 375 degrees F. Grease the bottom and sides of a 13" x 9" pan with vegetable oil.
In a bowl, add hash browns and vegetable oil. Mix until potatoes are evenly coated. Press potatoes into bottom and up sides of pan. Put into center of oven and bake for 20-25 minutes or until browned. Remove from oven and set aside.
In a mixing bowl, whisk together the eggs, milk, baking powder, salt and pepper. Add diced onion and mix. Pour egg mixture over pre-baked potatoes. Place two rows of sausage links on top egg mixture down the length of the pan. Cover and place in oven.
Bake for 30-35 minutes or until center is firm. Remove from oven, uncover. Top with cheese and parsley. Return to oven uncovered and bake an additional 5-10 minutes or until cheese is melted. Remove from oven; allow to set 5-10 minutes before serving.