Add potatoes to a large pot and cover with cold water. Salt the water and bring to boiling; reduce heat. Cover and cook for 10 minutes or until just tender. Meanwhile, place oil, 1/2 cup basil, and garlic in a small saucepan over medium-low heat while potatoes cook. Drain potatoes and set aside. Remove oil from heat and remove basil. In a blender combine the oil, vinegar, lemon juice, mayonnaise, salt, and pepper. Cover and blend until smooth. Transfer potatoes to serving bowl. Pour dressing over potatoes and gently toss to coat; cover and set aside.
Heat a gas or charcoal grill over medium heat. Add yellow peppers to grill rack. Cover and grill for 7 to 10 minutes or until charred, turning occasionally. Remove and cool slightly. Halve peppers, removing stems and seeds. Cut into large pieces. Add to potato mixture along with olives. Toss in remaining 1 cup basil. Serve warm or at room temperature.