Bring a large pot of salted water to a rolling boil. Add the pasta and cook until just al dente, about 8-10 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large deep skillet over medium heat. Add the minced garlic and sauté until fragrant, about 30 seconds, until it just begins to turn golden.
Add the chopped spinach to the skillet and cook until wilted and vibrant green, about 2-3 minutes. Use a slotted spoon to transfer the spinach to a bowl, leaving the garlic oil behind.
Lower the heat to medium-low. Pour the heavy cream into the skillet and stir in the smoked paprika. Whisk gently as the cream warms and begins to thicken slightly, about 2-3 minutes, releasing a warm smoky aroma.
Return the wilted spinach to the skillet and stir in the grated Parmesan cheese until melted and the sauce is smooth. If it gets too thick, add a splash of reserved pasta water to loosen it up.
Toss the drained pasta into the skillet, stirring well to coat each piece with the creamy, smoky sauce. Cook together for 1-2 minutes to meld flavors and warm through.
Season with salt and freshly ground black pepper to taste. Remove from heat and let sit for a minute to allow the sauce to thicken slightly.
Serve immediately, garnished with extra Parmesan or fresh herbs if desired. Enjoy the warm, creamy, smoky goodness in every bite!