1. In a small saucepan, heat the peanut oil over medium-high heat. Fry the potatoes, a handful at a time, until golden brown, then transfer to paper towels to drain. Repeat with the leeks, carrots, and green onions, frying each vegetable separately. Toss the vegetables together in a large bowl, season with salt and pepper to taste, and set aside.
2. Season the shrimp all over with salt and pepper to taste. In a large skillet, heat the olive oil over high heat. Sauté the shrimp, being careful not to crowd the pan, until pink, about 2 minutes per side. Set aside.
3. Place the salad greens in a large bowl, add all but 2 tablespoons of the Mint Dressing, and toss well.
4. To serve, arrange the salad in the center of a serving platter. Sprinkle shrimp with the remaining dressing and arrange around the edges of platter. Top the greens with a nest of the fried vegetables and serve.
Note: The shrimp can be barbecued or grilled for even more flavor.