Fratercula corniculata - The Horned Puffin
The “horns” of the horned puffin are the fleshy protuberances above the eyes. Check out the parts of the face in Fig. 4 (the bill plates on the beak and the horns around the eyes). Those are grown during the breeding season and shed each year.
Bulletin de la Societe Zoologique de France pour l’Annee 1879.