Pour 1/4 cup of the coconut milk into a large skillet and heat over medium. Add the ginger, carrots, bell pepper, and broccoli. Cover and cook, stirring occasionally until vegetables begin to soften up, about 3 to 4 minutes.
In a separate skillet, add a small amount of cooking oil (I use coconut oil) and heat to medium. Add the chopped chicken and sprinkle liberally with sea salt. Cook, stirring occasionally, until much liquid has seeped out of the chicken, about 5 minutes (note: you do not need to cook the chicken through, just until much of the liquid has cooked out).
Strain the liquid from the chicken and add the chicken to the skillet with the vegetables, along with the remaining coconut milk and curry paste. Stir well, cover, and cook 10 to 15 minutes, until chicken has cooked through and vegetables reach desired done-ness.
Serve curry with choice of rice, zucchini noodles, spaghetti squash, etc.