This is a single site trial of psilocybin therapy for the treatment of refractory Anorexia Nervosa in young adults. The psilocybin therapy will include three preparatory sessions, psilocybin dosing session one (20mg), two integration sessions, psilocybin dosing session two (up to 30mg), and four final integration sessions. Eating disorder symptoms will be measured pre and post treatment. Two family members of each young adult participant will be enrolled in the study. One of which will be required to attend a portion of two preparatory sessions and a portion of two integration sessions and receive psychoeducation about supporting the young adult participant through preparation and integration for psilocybin therapy. Investigators hypothesize that psilocybin will increase cognitive flexibility and that this increase will predict long-term changes in cognitive rigidity, habitual eating, and exercise behaviors in patients with Anorexia Nervosa.