Heat oil and butter in a pot over medium-low heat. Add chopped leek, carrots, celery, and bay leaves with a pinch of salt. Cover and sweat for 10 minutes, stirring occasionally. Do not let the veggies brown.
Add curry powder and quail and stir for 2 minutes. Add water and bring it to a boil, then cover it and lower the heat. Simmer for 10 minutes. Next, remove the quail from the pot; when they are cool enough to handle, remove the meat from the bones. Return the bones to the soup and allow it to simmer, covered, for 1 hour and 30 minutes. Meanwhile, cover and refrigerate the quail meat.
Peel, core, and cut the apple into bite-size pieces. After 1.5 hours, discard quail bones. Add the apple and rice to the pot and simmer until tender, about 15 minutes, stirring occasionally.
Return quail meat to the pot. If desired, add more water (or chicken stock) to thin out the soup. Stir in heavy cream and season to taste with chicken bouillon powder and freshly ground pepper. Ladle into bowls and garnish with minced chives.