Cook the spaghetti according to the package directions. If you want al dente pasta, cook for a minute or two less. Drain once cooked, reserving 1/2 cup of the pasta water.
While the pasta is cooking, make the sauce. In a large skillet over medium heat, add the olive oil. When the oil is shimmering, add the turkey and break up with a spoon. Cook, stirring every now and then, until browned, about 5 minutes.
Add the garlic and cook, stirring, for 1 minute. Add the rosemary and tomato paste and cook, stirring, for another minute. Add tomato sauce and Worcestershire and stir to combine. Simmer over medium low heat for at least 5 minutes, or until your pasta is ready. Season to taste with salt and pepper.
Off heat, add the drained pasta to the skillet and stir well to combine. If the sauce seems a bit dry, stir in some of the pasta water, a little at a time, until the consistency is to your liking.
Serve right away with grated parmesan, if desired.