In a medium skillet, heat 2 tablespoons oil over medium-high heat. Add onion and celery and cook, stirring occasionally, until vegetables begin to brown, 5 to 7 minutes. Remove from heat.

Meanwhile, in a large Dutch oven or heavy wide pot, heat remaining 2 tablespoons oil over medium-high heat. Add boar; cook, stirring frequently, until liquid has evaporated and meat is browned, about 15 minutes. Add browned vegetables, broth, wine and 1/2 teaspoon salt to pot, then add enough water to just cover meat. Bring to a simmer, then reduce heat to lowest setting, cover and very gently simmer 2 1/2 hours.

Uncover pot and, if necessary, continue to very gently simmer ragù until liquid is reduced to about 1 cup, 10 to 20 minutes more. Remove from heat and cover to keep warm.

Bring a large pot of salted water to a boil. Add pasta and cook until just tender, 2 to 3 minutes (if using dried pasta, cook until al dente). Drain, add to pot with ragù and toss. Serve immediately, passing cheese at the table.