Mix cumin, coriander, paprika, turmeric, black pepper, salt, and cayenne together in a small bowl for the spice blend.

Coat chicken breasts generously on both sides with about 1/2 of the spice blend and refrigerate, 2 to 12 hours. Reserve remaining spice blend until needed.

Cut broccoli florets off the stems. Slice the stems into strips, and then into 1/4-inch cubes, and reserve. Cut the florets into 1-inch pieces and set aside.

Heat butter and olive oil in a deep skillet or saucepan over medium-high heat. Add the chicken breasts and brown well, about 3 minutes on each side. Transfer onto a plate and let cool enough to handle, about 10 minutes.

While chicken cools, add garlic to the pan drippings. Cook and stir over medium-high heat for 30 seconds. Stir in the remaining spice blend and toast for 30 seconds. Pour in coconut milk and stir in ketchup, making sure to scrape up any bits from the bottom of the pan. Bring to a simmer; reduce heat to medium, stir in chicken broth, and let simmer until reduced, about 10 minutes.

Stir cubed broccoli stems into the sauce and cook until almost tender, 5 to 7 minutes.

Meanwhile, cut chicken breasts into 1/2-inch strips, and then into 1/2-inch cubes.

Increase skillet heat to medium-high and add broccoli florets. Cover and cook until almost tender, 3 to 4 minutes. Add chicken, and cook, stirring, until chicken is no longer pink in the center, and the broccoli is just fully tender, about 3 minutes. Taste and adjust seasoning. Serve immediately. Top with thinly sliced green onions.