Toss 2 teaspoons of the minced garlic, the shrimp, 1 tablespoon of the olive oil, and a 1/4 teaspoon of salt in a medium bowl. Let the shrimp marinate at room temperature for 20 minutes.
Heat the smashed garlic cloves and the remaining 2 tablespoons olive oil in a 12-inch skillet over medium-low heat, stirring occasionally, until the garlic is light golden brown, 4 to 7 minutes. remove the skillet from the heat and use a slotted spoon to remove the garlic from the skillet; discard the garlic. Set the skillet aside.
Bring 4 quarts of water to a boil in a large Dutch oven over high heat. Add 1 tablespoon salt and the pasta. Cook, stirring often, until just al dente. Drain the pasta, reserving 1/4 cup of the cooking water, and transfer the pasta back to the pot.
Meanwhile, return the skillet with the oil to medium heat; add the shrimp with the marinade to the skillet in a single layer. Cook the shrimp, undisturbed, until the oil starts to bubble gently, 1 to 2 minutes. Stir the shrimp and continue to cook through, about 1 minute longer. Using a slotted spoon, transfer, the shrimp to a medium bowl. Add the remaining 3 teaspoons of minced garlic and the red pepper lakes to the skillet and cook until just fragrant, about 1 minute. Add the flour and cook, stirring constantly, for 1 minute; stir in the vermouth and cook for 1 minute. add the clam juice and chopped parsley; cook until the mixture starts to thicken, 1 to 2 minutes. Remove skillet from the heat; whisk in the butter and lemon juice. Add the shrimp and sauce to the pasta, adjusting the consistency with up to 1/4 cup of reserved pasta cooking water. Season with pepper to taste.
Serve, passing the lemon wedges separately.