Special equipment: a large (15-inch) paella pan
For the aioli: Add the garlic, paprika and a pinch of salt to the bowl of a food processor. Pulse until the garlic is finely chopped. Add the lemon juice and egg yolks and pulse until combined.
With the motor running, slowly add the oil in a thin stream. Do not rush this step; it should it should take about 1 minute. If the oil is added too quickly, the aioli may break. Season with more salt and lemon juice as needed. Serve cold or at room temperature. The aioli may be stored in the fridge for up to 2 days.
For the shrimp stock: Combine the shrimp heads and shells and 2 cups water in a small saucepot. Bring to a simmer over medium-high heat and cook for 10 minutes. Turn off the heat and stir in the saffron. Let sit for 5 to 10 minutes to allow the saffron time to infuse the stock. Strain the shrimp stock and reserve.
For the fideos: Set a paella pan over medium heat and coat with 2 tablespoons of the olive oil and all of the butter. Add the vermicelli and toast, stirring regularly, until light golden brown, about 5 minutes; do not walk away during this step, as the noodles can burn easily. Transfer the noodles to a bowl.
Coat the paella pan again with another 2 tablespoons of the olive oil, add the chorizo and cook until the spices from the sausage begin to color the oil. Add the onions and cook until softened and aromatic, about 5 minutes. Add the garlic and cook 1 minute more. Add the smoked paprika and red pepper flakes and season with salt. Add the wine and cook until reduced by half. Add the tomatoes and cook until almost all of the liquid has evaporated, 5 to 6 minutes.
Set an oven rack in the middle position and preheat the broiler.
Add the toasted vermicelli, the reserved shrimp stock and the chicken stock; it should come to 4 cups total liquid. Lower the heat to medium and cook until all liquid has been absorbed, 15 to 20 minutes, stirring every few minutes.
Season the shrimp with salt and toss with the remaining 2 tablespoons olive oil. When the noodles are cooked but still have a little al dente bite to them, stir in the asparagus, then arrange the shrimp and mussels on top of the noodles. Transfer the paella pan to the oven and broil until the top is golden brown and crispy, 8 to 10 minutes; rotate the pan halfway through for even browning. Watch closely during broiling to prevent burning. You'll know the paella is ready when the top of the spaghetti is nicely browned, the shrimp are bright pink and the mussels have popped open. Garnish with the parsley and serve with lemon wedges and smoked paprika aioli.
Recipe courtesy of Kelsey Nixon