Make the saffron-clam broth.

1. Toast the saffron until fragrant in a small saucepan set over medium-low heat (30–60 seconds). Remove from the heat and crush the saffron as finely as possible, using the back of a spoon. Add the clam juice and bring to a boil over high heat. Immediately remove from the heat and set aside to infuse.

Make the sofrito  

1. Halve and peel the onion. Grate the onion halves on the largest holes of a box grater to get about 1/3 c of onion puree. Cut the tomato in half horizontally (not through the stem). Position the box grater over a shallow bowl and gently grate the tomato halves all the way down to the skin to get about 1 ¼ cups of juicy tomato pulp.
2. Set a 15-inch paella pan over medium-low heat and add ¼ c of the oil. When it’s hot, add the grated onion.  Cook the onion in the centre of the pan, stirring occasionally, until it softens and darkens slightly (4 minutes). Stir in the tomato pulp, chopped garlic, smoked paprika and ¼ tsp salt. Gently cook the mixture in the centre of the pan, stirring frequently, until it’s deep, dark red and very thick (30–40 minutes). Adjust the heat as needed, being careful not to let it burn. If it sticks, deglaze by adding a little water and scraping the pan.

Make the shrimp-mussel broth.

1. While the sofrito cooks put the shrimp shells in a 4-quart saucepan, stir over medium heat until they’re dry and pink (2–3 minutes). Add 5 cups of water and bring to a boil.
2. Pick through the mussels to find the smallest dozen. Remove the beards if necessary, and reserve the mussels in the refrigerator. Add the remaining mussels to the boiling water. Cover, reduce the heat to low and simmer for 10 minutes. Strain the broth into a 2-quart liquid measure, discarding the shells and mussels. Add the saffron-clam broth and add 1 ½ tsp salt to the shrimp-mussel broth. Measure out 5 ¼ cups of the broth and reserve the remainder.
3.  

Brown the chicken and chorizo

1. In a 10-inch skillet, heat 2 tbsp of olive oil; brown and partially cook the chicken thighs, starting with the skin side down (10 -12 minutes). Remove from pan and set aside. 
2. Brown the sliced chorizo sausage (3 minutes); set aside. 
3. Pour off fat from the pan. Use about a cup of the 5 ¼ cups of broth to deglaze the pan, then return the broth to the 5 ¼ cup mixture.

Make the paella

1. When the sofrito is done, add the rice to the paella pan and cook briefly over medium heat, stirring constantly to combine it with the sofrito (1-2 minutes). Spread the rice evenly in a thin layer across the bottom of the pan.
2. Increase the heat to high and slowly pour in the 5 ¼ cups of broth—try not to disturb the rice, so it stays in an even layer. From this point on, do not stir the rice.
3. Bring to a boil and then adjust the heat to maintain a vigorous simmer, repositioning the pan as needed so it bubbles all the way to the edges (the bubbles at the edge will be smaller than the bubbles at the centre).  Simmer vigorously until the rice appears at the level of the broth (about 8 minutes).
4. Arrange the chicken breasts, the chorizo sausage and the mussels in the pan, distributing them evenly.  Lower the heat, so the broth maintains a more moderate simmer, and after another 5 minutes, arrange the shrimp in the pan, pushing them into the rice. Continue simmering until the liquid is absorbed and the rice is tender but still firm—taste a few grains below the top layer (about 3 minutes more). 
5. Scatter the sugar snap peas over the surface of the paella, cover the pan loosely with foil, and simmer until the vegetables are tender and the rice is cooked through (about 2 more minutes).  Note: The rice needs to simmer for about 18 minutes in total.  If at any point the broth seems to be evaporating too quickly, reduce the heat slightly, cover loosely with sheets of foil, or add a little more broth or water, ¼ c at a time as needed.  Also, if the chicken thighs, mussels or shrimp are still undercooked by the time the rice is done, cover loosely with foil for a few more minutes to trap the heat and finish the cooking.
6. Check for any caramelised rice sticking to the pan by using a spoon to feel for resistance on the bottom of the pan.  Check several areas, especially in the centre of the pan. If there is none, increase the heat to medium-high and carefully cook, moving the pan around, until you hear a good deal of crackling and feel resistance (1-2 minutes).  If you smell burning, immediately remove the pan from the heat.
7. Remove the pan from the heat, cover with the foil, and rest (5-10 minutes). 
8. Arrange the lemon wedges around the perimeter of the pan and serve.