1. Halve leeks lengthwise, then coarsely chop. Wash in a bowl of cold water, agitating them, then dry on paper towels.
2. Melt butter with oil in a medium (2- to 3-quart) saucepan over medium heat until foam subsides. Cook leeks with ginger and 1/2 teaspoon salt, stirring, until softened (6-8 minutes). Transfer half of leeks to another medium saucepan.
3. Add celeriac and half of chopped apple to one of the saucepans and cook, stirring, 2 minutes. Add 2 cups broth, 2 cups water, and simmer, covered, until celeriac is very tender (about 30 minutes).
4. Add beets and remaining chopped apple to the other saucepan. Stir in remaining 2 cups broth and 1 cup water and simmer, covered, until beets are tender (about 30-40 minutes).
5. Purée celeriac soup with an immersion blender (or in batches in a blender) until smooth. (Use caution with hot liquids.) Return soup to cleaned saucepan. If thick, stir in 1/2 to 2/3 cup water. Season with 1/4 teaspoon each salt and pepper and keep warm.
6. Purée beet mixture as above. Stir in remaining 1/4 teaspoon each salt and pepper.
7. Serve soups separately in small cups, garnishing beet soup with celery leaves, and celeriac soup with a drizzle of beet soup.