Heat a large heavy pot over medium-high heat. Add the coconut oil, soften the onion then add the curry paste and stir for about 1 minute, or until fragrant. Meanwhile take the hard outer layer from the lemongrass stick and then bash with the back of your knife to release the flavor and add to the pot along with the lime leaf.
Add the squash and stir to coat with the curry paste. Stir in the chickpeas. Add the coconut milk and ½ cup water and bring to a simmer.
Reduce the heat to medium-low, cover, and simmer gently for about 10 minutes, or until the squash just begins to soften.
Stir in the red pepper, broccoli and gently simmer, uncovered, stirring occasionally, for about 10 minutes, or until the squash is tender but not falling apart and the sauce has reduced slightly. Season to taste with freshly ground pepper and fish sauce.
Remove the lemongrass and lime leaf and stir through the spinach leaves. Divide the curry among four soup bowls, top with chopped coriander, and serve.