Whisk in curry paste until well combined, about 1 minute. Gradually whisk in coconut milk and broth, and cook, whisking constantly, until incorporated, about 1-2 minutes. Add honey and stir.
Turn the stove up to high and bring to a boil; add rice, reduce heat to medium low and simmer until rice is cooked, about 25 minutes. Add shrimp and cook for about 4 minutes or until pink.