Place ground turkey in a bowl. Lightly mix in garlic, parsley, thyme, oregano, and salt and pepper to taste. Form ¾-inch meatballs, moistening your palms with cold water, and place the meatballs on a plate lined with wax paper. Chill for ½ hour.
Heat the olive oil in a large nonstick skillet over medium-high heat. Working in batches, brown the meatballs, rolling and turning them for 5 or 6 minutes. Pour off the fat, leaving the browned bits in pan.
Add tomato sauce to the skillet and bring to a simmer. Add meatballs and any juices to sauce. Cover and simmer about 3 minutes, stirring gently, until the meatballs are just cooked through. Stir in chopped parsley and correct the seasonings.
Meanwhile, boil the spaghettini in salted water until tender. Drain. Arrange in 4 shallow bowls, spoon the meatballs and sauce over, sprinkle with Parmigiano-Reggiano, and garnish each bowl with a parsley sprig.