Melt the coconut oil in a large pot at medium-high heat. Add the onion, break it up a bit with a spoon and cook until soft (about 5 minutes), stirring often.
Add the next 5 ingredients and stir together for about 1 minute. Add the coconut milk and vegetable stock. Stir together, bring to a boil and reduce heat to low. Lightly simmer for about 10 minutes.
Add the soy sauce, fish sauce, carrots, and broccoli. Increase heat to high and bring to a boil. As it starts to boil, add the shrimp and reduce heat back to low. Stir together and continue cooking until the shrimp turns pink and the vegetables are tender (about 3 minutes).
Turn off the heat. Add the lime juice and cilantro. Adjust the seasoning if necessary with a pinch of salt, more lime juice, or more curry paste/powder for additional heat.