Heat oil in paella pan or large skillet over medium-high heat. Pat dry shrimp, sprinkle with 1/4 tsp salt and cook in a single layer until golden underneath. Flip and cook until just opaque. Transfer to a plate.
Add chorizo and chicken thighs to the same pan. Season chicken with 1/2 tsp salt. Cook until browned then add the onion plus ¼ tsp more salt. When onion is soft, stir in garlic and smoked paprika; cook another 2 minutes.
Add tomato, saffron, broth, wine, ¾ tsp more salt and the pepper, stir, then add the rice and cook, covered, until most of the liquid is absorbed, about 15 minutes. Top with shrimp and sprinkle with parsley to serve.
Video
Notes
A true paella pan is not necessary but I do love the large surface area and how it makes lots of crispy bits on the bottom of the paella. Mine is this one from Le Creuset.
Swap in thawed pre-cooked shrimp for an easy shortcut and just stir them in to heat through at the end.
Fresh chorizo is not as good as the cured (already cooked) kind. Fresh doesn't render as much flavourful oil and it dries out with the long cooking time.
If you don't have saffron (it's pricey), just leave it out.