This phase II trial tests the safety, side effects, best dose and activity of tovorafenib (DAY101) in treating patients with Langerhans cell histiocytosis that is growing, spreading, or getting worse (progressive), has come back (relapsed) after previous treatment, or does not respond to therapy (refractory). Langerhans cell histiocytosis is a type of disease that occurs when the body makes too many immature Langerhans cells (a type of white blood cell). When these cells build up, they can form tumors in certain tissues and organs including bones, skin, lungs and pituitary gland and can damage them. This tumor is more common in children and young adults. DAY101 may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Using DAY101 may be effective in treating patients with relapsed or refractory Langerhans cell histiocytosis.