Melt butter in a large Dutch oven over medium. Add leeks, carrots, celery, and garlic. Cook, stirring often, until softened, about 5 minutes. Add flour; cook, stirring constantly, 1 minute. Add broth, chicken, and thyme. Bring to a boil over medium-high. Reduce heat to medium-low, and simmer 10 minutes. Stir in collard greens; cook until just tender, about 5 minutes. Remove from heat; stir in cooked rice, cream, salt, and pepper. Garnish servings with additional thyme.