In a large bowl, stir together all jerk seasoning ingredients.
Mix 1 tablespoon oil into the spice mix, then add the shrimp and stir around until well coated. Cover the bowl and marinate the shrimp in the fridge for 20 minutes.
While the shrimp are marinating, bring a large pot of water to a boil and cook the pasta.
Once the shrimp had 20 minutes in the marinade, make the sauce: Heat the remaining oil in a large non-stick pan, then add the diced onion and saute until translucent (about 2 minutes).
Stir in the shrimp along with any marinade that's still in the bowl. Cook until the shrimp are just starting to turn pink (3 to 4 minutes).
Stir in chicken broth, tomato paste and cream. Bring to a simmer and cook until the sauce has thickened a bit (about 5 minutes after it starts to simmer).
Stir in lime zest and juice and season to taste with more lime juice. Mix the sauce with the pasta, sprinkle with roughly chopped fresh thyme leaves and serve.
