The correct answer is E. Pachyonychia congenita.

The hamartomatous cyst in multiple locations is consistent with a diagnosis of steatocystoma multiplex. This condition is associated with mutations in keratin 17 and is highlighted in the condition pachyonychia congenita.

Congenital adrenal hyperplasia, Gardner syndrome (epidermal inclusion cyst), Loeys-Dietz syndrome, and mutilating palmoplantar keratoderma (Olmsted syndrome) are not associated with steatocystoma multiplex.