Heat the peanut oil in a large skillet over high heat to 375 degrees F. Fry the plantain slices in batches until crisp. Drain on paper towels and reserve. Heat a grill or grill pan. Brush the squid with olive oil and season to taste with salt and pepper and grill for 3 minutes on each side. Cut into 2-inch pieces.
Mint-Smoked Chile Vinaigrette:
Combine all ingredients in a blender and blend until smooth. Season with salt and pepper.
Assembly: Toss the squid, mangoes and arugula with the vinaigrette in a large bowl. Heap the salad onto a large platter and garnish with the fried plantains, red pepper and mint leaves.