Melt butter; toss with bread on a baking sheet. Bake at 350° for 20 minutes or until golden.
Heat oil in a Dutch oven over medium heat. Add leek; cook 10 minutes, stirring often. Stir in flour; cook 2 minutes, stirring well. Add celeriac and broth; bring to a simmer. Cook for 30 minutes. Let stand 10 minutes.
Place half of mixture in blender. Remove center piece of blender lid, and secure blender lid on blender. Place a clean towel over opening in lid. Process until smooth. Strain pureed mixture through a sieve over a bowl; discard solids. Repeat procedure with remaining celeriac mixture.
Return soup to pan over medium heat; stir in half-and-half, pepper, and salt. Cook for 5 minutes. Serve with croutons. Garnish with parsley, if desired.