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Rinse the squash, remove the ends and pits and chop into halved slices. Divide broccoli into florets, not too small. Grate the peel of a lime and squeeze its juice.
Remove any excess fat or muscles of the chicken breast and divide them into cubes. Drain the chick peas if needed.
Heat a dash of oil in a large skillet and cook the chicken cubes for a few minutes. Add squash and after a few minutes also the broccoli florets.
Also add the red curry paste and after a few minutes also chick peas along with coconut milk. Bring to a boil and as soon as it starts to boil, you'll turn the the heat.
Let is simmer for about 30 minutes and then also add the lime zest and juice along with sesame oil. As soon as the vegetables are soft enough you can season the curry with pepper and salt.
Serve with rice or savory crepes and finish the curry with sesame seeds and fresh parsley. Enjoy!