Bring a large pot of salted water to a rolling boil. Add the spaghetti and cook until just al dente, about 8 minutes. Drain, reserving about ½ cup of pasta water, and set aside.
While the pasta cooks, peel and devein the shrimp if not already done. Pat them dry and set aside.
Mince the garlic cloves finely. Zest the lemon and juice it, keeping both separate.
Heat the olive oil in a large skillet over medium heat until shimmering. Add the minced garlic and sauté for about 30 seconds until fragrant, stirring constantly to prevent burning.
Add the shrimp to the skillet. Cook for about 2-3 minutes per side until they turn bright pink and slightly opaque, filling the kitchen with a sweet, briny aroma.
Sprinkle the smoked paprika over the shrimp and stir to coat evenly. Pour in the lemon juice and add the lemon zest, cooking for another 30 seconds to meld the flavors.
Reduce the heat to low, then add the drained spaghetti to the skillet. Toss gently with tongs to coat the pasta in the lemon-garlic sauce, adding reserved pasta water a tablespoon at a time to loosen the mixture and create a glossy coating.
Season with salt and pepper to taste. Toss in the chopped parsley if using, for a fresh herby finish. Give everything a final gentle toss to combine all the flavors.
Serve immediately on warm plates, garnished with extra lemon wedges and parsley if desired. Enjoy the bright, smoky, tender shrimp with flavorful pasta in every bite!