Bring a 6- to 8-quart pot of salted water to a boil over high heat. Add the pasta and cook according to package directions until al dente. Drain in a colander.
Meanwhile, heat the oil in a 6- to 8-quart Dutch oven (or other heavy-duty pot) over medium-high heat until shimmering hot. Scatter the country ham in the pot and cook, stirring occasionally, until the pieces are just beginning to brown and have rendered some fat, 3 to 4 minutes. With a slotted spoon, transfer half of the ham to paper towels to drain; set aside. If the pot appears dry, add another tsp. of oil.
Add the garlic and red pepper flakes and cook, stirring, until the garlic is fragrant but not browned, about 30 seconds. Add the wine and 2 cups of water, cover, and bring to a boil. Add the sweet potato and return to a vigorous boil. Cover and continue to cook until the potato is soft at the edges but still firm in the center, about 5 minutes.
Add the clams, stir to distribute evenly, cover the pot, and continue to cook, stirring once or twice, until the clams have opened, 5 to 8 minutes (discard any that don’t open).
Divide the cooked linguine among 4 pasta bowls, and top with half of the parsley leaves. Divide the clams, sweet potato, and broth evenly among the bowls. Garnish with the remaining parsley, the reserved country ham, and a lemon wedge (if using).