1. Place sliced leeks in a small bowl of cold water. Let stand for 5 minutes to rid them of dirt and sand. Lift sliced leeks out of water, leaving sand behind, and drain well. Bring a large pot of water to a boil over high heat.

2. Heat olive oil in large skillet over medium-low heat. Add leeks and garlic, and cook until softened, 2 to 3 minutes. Raise the heat to medium-high. Add chicken stock, cream, ham, and peas; season with salt and pepper. Let the sauce cook until it is reduced by half, stirring frequently until it has thickened, about 6 minutes.

3. Salt the boiling water, add pasta, and cook until al dente, about 4 minutes for fresh. Drain fettuccine, and return to pot. Add sauce to fettuccine, and toss to combine. Transfer to a serving dish, sprinkle with the mint, and serve.