Squid provides bold color and sophisticated flavor to this updated take on the traditional Valencian dish known as Fideua Negra.
Preheat oven to 375. Using a kitchen mallet, pound both sides of calamari bodies a few times. Insert a sharp knife into calamari bodies, cut along seam, and open like a book. Cut in half lengthwise, then on the diagonal into 1/2-inch-thick strips. (Leave tentacles whole, or halve if large.) Toss strips and tentacles with lemon juice in a nonreactive bowl.
Heat 1 tablespoon oil in a large saute pan or a 13-inch paella pan over medium-high heat. Working in two batches, add noodles, and cook, stirring, until golden brown, about 4 minutes. Transfer to a bowl. Reserve pan.
Bring stock and squid ink to a low simmer in a saucepan.
Heat butter and remaining tablespoon oil in the saute pan over medium heat. Add shallots and garlic, and cook, stirring occasionally, until soft, about 3 minutes. Add tomato and paprika, and cook, stirring occasionally, 5 minutes. Stir in noodles, calamari, stock mixture, 1 tablespoon parsley, salt, and pepper.
Transfer to oven. Bake until noodles on top begin to curl, about 10 minutes. Top with remaining tablespoon parsley, and drizzle with oil. Serve with allioli.