Heat oil in a pot over medium-high. Sauté onions, garlic, and ginger until onion is translucent, about 3-5 minutes.
"Bloom" the curry paste. Pour about 1/3 of the can of coconut milk into the pot, along with the red curry paste. Fry these together, stirring constantly, for about a minute. This will help you to get the most flavor out of the curry paste.
Add in the vegetable broth to deglaze the pot, scraping up any bits that might be sticking to the bottom.
Add in the rest of the coconut milk, the butternut squash, and the chickpeas. Bring to a boil, then reduce heat to low and simmer for 20 minutes, or until butternut squash is tender.
Bring the heat back up to medium and stir in the spinach. Cook for an addition 2-3 minutes, until the greens are wilted and the curry is warmed through.