Pat the shrimp dry with paper towels and arrange them in a single layer. Season evenly with kosher salt and black pepper.
Heat a large skillet over medium-high heat. Add the olive oil and butter.
Once the butter is melted and the pan is hot, add the shrimp in a single layer. Cook the shrimp without moving them for 2 minutes, allowing the bottoms to turn golden. Flip the shrimp and cook for another 1 to 2 minutes, until opaque and lightly browned. Transfer the shrimp to a bowl and continue with the sauce.
In the same skillet, add the garlic and cook for about 30 seconds, stirring frequently, just until fragrant.
Pour in the vermouth (or white wine) and lemon juice. Bring to a simmer and cook for 2 to 3 minutes, scraping up any browned bits from the bottom of the pan, until the liquid reduces slightly.
Stir in the lemon zest. Reduce the heat to low and whisk in the cold butter until melted and the sauce becomes glossy.
Return the shrimp and any accumulated juices to the skillet. Toss to coat in the sauce and cook for about 1 minute, just until heated through.
Stir in the chopped parsley.
Serve the shrimp and sauce over cooked spaghetti. (optional)