Pat the shrimp dry if needed. Season with salt and pepper and toss. Heat a large saucepan with 2 tablespoons olive oil over medium-high heat. Working in batches if necessary, sauté shrimp until lightly browned and just cooked through; transfer to a bowl and set aside.

Drain clams, reserving liquid in a 2-cup measuring cup; add water as needed to make 2 cups. Reserve. Coarsely chop clams and set aside.

Return saucepan to medium heat and add olive oil and butter. When melted, add garlic and cook, stirring often, until garlic is soft and fragrant, 2-3 minutes (do not brown). Add tomatoes and cook, stirring occasionally, until tomatoes begin to break down, 4-5 minutes. Increase heat to medium-high and add vermouth. Bring to a boil and cook until vermouth is almost evaporated. Stir in reserved clam juice, bring to a simmer, adjust heat, cover, and simmer for 30 minutes. Taste and adjust seasoning.

Meanwhile, cook pasta according to package directions. Drain and return to pot.

To finish, stir chopped clams and shrimp into sauce and heat through; add to pot with cooked pasta and heat over medium heat to meld flavors, about 30 seconds. Transfer to a serving bowl and garnish with parsley. Serve hot, passing grated Parmesan and hot pepper flakes at the table.