Melt butter in pot over medium-high heat. Add sliced celery, generous 3 cups diced pears, leek tops, bay leaves, and thyme. Cover; cook until celery softens, stirring occasionally, about 8 minutes. Toss in flour. Stir in 3 cups broth; bring to boil. Cover, reduce heat to medium-low, and simmer until celery is tender, about 20 minutes.
Remove bay leaves from soup. Puree soup in batches in blender until smooth. Return puree to same pot. Season to taste with salt and pepper. Thin with more broth by 1/4 cupfuls, if desired. Rewarm briefly.
Divide soup among bowls; garnish with 1/2 cup finely diced pear and celery leaves.