Heat oil in a 4 to 5 quart dutch oven or stock pot over medium until shimmering. Add the onions, carrots, celery and a big pinch of salt, and saute until soft, about 8 minutes.

Add the stock and bay leaf. Increase heat and bring to a gentle boil. Then reduce heat to maintain a simmer, cover, and cook for 20 minutes. Uncover, and remove the bay leaf at the end of the simmer.

While the turkey base simmers, fill a medium (2 quart) pot with water and a big pinch of salt, and bring to a boil. Add the orzo, adjust heat to maintain a gentle boil, and cook according to package directions (times will vary depending on the type of orzo you chose). Drain and add to the stock, along with the turkey, at the end of the 20 minute simmer. Reduce heat under the soup to low. Taste and add salt, if necessary.

In a medium mixing bowl, whisk the eggs and lemon together until very smooth. With your free hand, slowly add two ladles of soup, one at time, to the egg mixture, whisking vigorously and continuously until completely incorporated. Then add the egg mixture to the soup, whisking the soup until incorporated. The soup should have lightened considerably in color and have a silky texture. (Do not let the soup come to a boil after adding the eggs - ditto for reheating: use a medium-low-low setting to bring the soup up to eating temperature.) Taste and add salt and white pepper (if using). Garnish with the chopped parsley.