Heat olive oil in a saucepan over medium heat. Transfer sausage links into the hot pot. Cover with a lid and cook until beautifully browned and just barely cooked through, about 5 minutes per side. You can increase the heat a little if you like, but make sure the oil does not smoke. Turn off the heat and remove sausages to a plate to cool completely.

While the sausages are cooling, add wine to the same pot over medium-high heat. As it comes up to a simmer, stir the caramelized bits on the bottom of a pan with a spoon or spatula. Simmer until it reduces by about half, 1 to 2 minutes.

Add marinara sauce. Pour water into the jar of pasta sauce, seal, and shake to rinse out the jar. Pour that liquid into the pot and return to a simmer. Reduce heat to low.

Slice each fully cooled sausage into 4 pieces. Transfer sausage and any accumulated juices into the simmering sauce. Stir and increase heat to just between low and medium-low. Cook at a gentle, steady simmer, stirring occasionally, for 1 hour. Taste and adjust seasonings. Skim about 1/2 of the fat from the surface, and continue to cook until reduced and thick, about 30 minutes longer.

Meanwhile, bring a large pot of generously salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until almost tender yet firm to the bite, 10 to 11 minutes. Drain spaghetti and transfer it directly into the pot of hot sauce. Mix until thoroughly combined. Cover with the lid and let sit for 1 minute so the pasta can absorb some of the sauce.

Evenly divide pasta onto 4 plates and top each serving with 4 pieces sausage. Sprinkle with Parmigiano-Reggiano and parsley.