Scrub oysters with a stiff brush under running water. Insert an oyster knife into the hinged edge of each oyster; twist knife handle back and forth until top shell is loose. Slide oyster knife along the bottom of the shell to detach muscle. Remove and discard top shell; drain and reserve 1 cup oyster liquor. Keep oysters in the deeper bottom shell. Arrange oysters over rock salt in a jellyroll pan; chill.
Combine 1 cup oyster liquor, 1 cup cream, and next 5 ingredients in a small saucepan. Bring to a boil; reduce heat, and simmer, uncovered, about 25 minutes or until thickened. Pour mixture through a wire-mesh strainer into a bowl. Stir in ham, celery, and pepper; set celery cream aside.
Cook celery root in boiling water to cover 10 minutes or until tender; drain. Place celery root, 1/4 cup cream, butter, and salt in a food processor. Process until smooth.
Place 1/2 teaspoon celery root puree under each reserved oyster in the shell. Top with 1 teaspoon reserved celery cream. Broil 3 inches from heat for 5 minutes or until bubbly. Serve immediately.