Preheat oven to 400°.
Combine florets and oil in a large bowl; toss to coat. Add thyme and salt; toss well. Arrange florets on a jelly-roll pan coated with cooking spray. Bake at 400° for 1 hour or until golden brown, stirring after 30 minutes.
Combine florets, 2 cups broth, and milk in a blender. Process 3 minutes or until smooth. Pour pureed mixture into a large saucepan. Add remaining 2 cups broth and pepper. Cook over medium heat until thoroughly heated. Garnish with fresh thyme sprigs, if desired.