Bring a large pot of generously salted water to a boil and cook your pasta until just al dente, following the package instructions. Right before draining, scoop out about half a cup of the starchy pasta water and set it aside. Drain the pasta and set it in the colander while you build the sauce in the same pot or a separate skillet.
Heat the olive oil in a large skillet over medium heat and add the diced onion. Cook for about 3 to 4 minutes until it turns soft and slightly golden around the edges. Stir in the minced garlic and smoked paprika, cooking for another 30 seconds just until fragrant, being careful not to let the garlic burn.
Pour in the chicken stock and heavy cream, stirring to combine everything in the pan. Let this simmer gently for 2 to 3 minutes so the sauce starts to thicken slightly and the flavors meld together. Season with a pinch of salt and pepper, tasting as you go so the sauce isn't under-seasoned.
Stir the chopped leftover turkey directly into the simmering sauce so it can warm through without drying out. Add the fresh baby spinach and let it wilt for about a minute, stirring gently so it's evenly distributed. The sauce should look creamy and coat the back of a spoon at this point.
Add the drained pasta straight into the skillet with the sauce and toss everything together using tongs or a spoon. If the sauce feels too thick, splash in some of that reserved pasta water a little at a time until it loosens up nicely. Keep tossing until every piece of pasta is coated in that creamy turkey sauce.
Sprinkle the freshly grated Parmesan over the top and give everything one final toss so the cheese melts into the sauce. Taste one more time and adjust the salt and pepper if needed before taking it off the heat. Serve immediately while it's hot, bubbly, and smelling incredible.