To make the Lemon Brodetto, warm the olive oil in a medium saucepan over medium heat. Add the shallots and saute until tender, about 7 minutes. Add the lemon juice, zest, and broth. Bring to a simmer, and keep warm, covered, over low heat.
To make the Pea Puree, combine the peas, mint, garlic, salt, and pepper in a food processor and puree. With the machine running, add the olive oil in a steady drizzle. Transfer the pea puree to a small bowl and stir in the Parmesan. Set aside.
To make the Salmon, warm the olive oil in a large, heavy skillet over high heat. Season the salmon pieces with salt and pepper. Sear the salmon until a golden crust forms, about 4 to 5 minutes on the first side. Flip the fish and continue cooking until medium-rare, about 2 minutes more depending on the thickness of the fish.
To assemble the dish, add the tablespoon chopped mint to the Lemon Brodetto and divide between 4 shallow dishes. Place a large spoonful of Pea Puree into the center of each bowl. Place a salmon piece atop each mound of Pea Puree. Serve immediately.