Place a skillet over medium heat with coconut oil, ginger, garlic, and onion. Saute for 3 minutes, or until the onion is translucent. Add in chicken and cook, stirring occasionally, until no longer pink (about 7 minutes.) Add in garam masala, chili, cumin, turmeric, broth, coconut milk, and tomato paste. Bring the sauce to a boil and then reduce to a low simmer. Stir in broccoli and cover. Cook for 6-7 minutes, or until the broccoli is soft.