Add water to a large stockpot and bring it to a boil. Add 1 tablespoon salt and add the pasta, cooking it according to package directions while you prep the rest of the dish.
Peel and devein the shrimp while the water boils.
Toss shrimp, parsley, 1 tablespoon of the olive oil, 1 tablespoon lemon juice, lemon zest, half the chopped tarragon, and half the minced ginger in medium bowl. Generously season the mixture with sea salt and ground pepper.
Heat 1 tablespoon oil in large skillet over medium heat. Add the shallots and sauté until soft, about four minutes. Add white wine and reduce let reduce for two minutes. Add shrimp. Saute until almost cooked through, about 3 minutes. Add butter and cream; bring just to simmer. Add remaining 1 teaspoon ginger. Season with salt and pepper. Set shrimp aside in another bowl, scraping out most of the pan’s contents.
Put the pan back on medium-high heat. Add remaining 1 tablespoon oil in large nonstick skillet. Add spinach and remaining 1 tablespoon lemon juice; sprinkle with salt and pepper. Toss until just wilted, about 25 seconds.
Add the cooked spaghetti and vegetable stock. Stir and mix into the pasta. Mound spinach pasta mixture in center of plates top with shrimp and sauce. Sprinkle shrimp with remaining 2 teaspoons tarragon. Serve warm.