Place the cubed chicken in a mixing bowl and pour in the 1/2 cup coconut milk; season with sea salt and black pepper and stir to coat. Refrigerate for at least 20 minutes while you prep the vegetables.
Heat the coconut oil in a large high-sided frying pan over medium-high heat. Add the minced ginger, ground cumin, ground coriander, and ground cardamom and cook, stirring, until fragrant and slightly golden, about 20 seconds.
Add the marinated chicken to the pan in a single layer, shaking off excess coconut milk but leaving some coating on the pieces. Reserve any leftover coconut milk. Cook, turning as needed, until the chicken is cooked through and no longer pink, about 4–5 minutes.
Add the broccoli florets and cook for 1 minute over medium-high heat. Reduce the heat to medium, then add the spiralized carrot noodles and the remaining 1/2 teaspoon sea salt. Stir and cook until the carrot noodles are tender, about 4 minutes, stirring frequently.
Pour in the reserved coconut milk, stir to combine, and cook for about 30 seconds until heated through. Remove from heat.
Garnish with cilantro and serve immediately.
