Prepare Shrimp
Cut shrimp in half crosswise. Toss with salt and baking soda. Let stand 10 minutes to 1 hour.
Cook Shrimp
Heat 3 tablespoons olive oil over high heat until shimmering. Cook shrimp until pink and lightly golden, about 2 minutes. Transfer to a plate.
Make Sauce
Add 3 tablespoons olive oil to skillet. Cook garlic and red pepper flakes over medium-high heat until garlic is golden, about 1 minute.
Add vermouth. Boil over high heat until reduced by half, about 4 minutes.
Add butter. Stir and swirl pan rapidly as butter melts to emulsify sauce. Remove from heat. Add lemon juice and season with salt.
Cook Pasta
Cook pasta in salted boiling water until 2 minutes shy of al dente.
Transfer pasta to skillet with sauce, reserving pasta cooking water. Add ¼ cup pasta water. Cook over high heat, tossing rapidly, until al dente and sauce coats noodles, 2-3 minutes. Add more pasta water as needed.
Finish Dish
Return shrimp to skillet with juices, lemon zest, parsley, and remaining 2 tablespoons olive oil. Toss to combine. Remove from heat. Season with salt if needed.
Divide pasta and shrimp among bowls and serve.
