Re-differentiation of Radioiodine-Refractory BRAF V600E-mutant Papillary Thyroid Carcinoma With GSK2118436

Inclusion Criteria: * Histologically confirmed papillary thyroid carcinoma, including its variants, such as tall cell PTC or poorly differentiated thyroid carcinoma, that is metastatic or unresectable AND harbors a BRAF V600E mutation * Evaluable disease, as defined by at least one lesion that can be accurately measured in at least one dimension on CT scan or ultrasound, if present in the neck * Radioiodine-refractory disease * Life expectancy \> 6 months * Able to swallow and retain oral medication * Normal organ and marrow function Exclusion Criteria: * Pregnant or breastfeeding * Previous treatment with a specific BRAF or MEK inhibitor * Receiving any other study agents * Known brain metastases * History of allergic reactions attributed to compounds of similar chemical or biologic composition to GSK2118436, bovine TSH, mannitol or iodine * Active gastrointestinal disease or other condition that will interfere significantly with the absorption of drugs * History of known glucose-6-phosphate dehyrogenase (G6PD) deficiency * Corrected QT interval \>/= 480 msecs; history of acute coronary syndromes (including unstable angina), coronary angioplasty, or stenting within the past 24 weeks; Class II, III, or IV heart failure, abnormal cardiac valve morphology; or history of known cardiac arrhythmias * Taking herbal remedies * Subjects with significant symptoms from their thyroid cancer, or have a large burden of rapidly progressive iodine-refractory PTC who are in need of other …