Put a large pot of salted water on to boil for the pasta.
Heat the olive oil in a pan over medium heat and add the carrot and onion. Sauté until the carrot is soft and the onion translucent, 3 to 4 minutes. Add the garlic and cook until fragrant, 1 to 2 minutes longer.
Add the lamb and cook, breaking up chunks with a spatula, until lightly browned, 5 minutes. Add the tomatoes and wine, season to taste with salt and pepper and simmer for 5 minutes, stirring occasionally.
While the lamb simmers, cook the pasta according to package directions, drain and toss with a drizzle of olive oil.
Add the leeks to the ragu and cook just long enough for them to soften, 2 to 3 minutes. Taste and adjust the seasoning if necessary. Add the chopped parsley just before plating.
Divide the pasta between 4 plates and top with the ragu. Serve immediately.