1. Bring large pot of water to a boil. Add green beans; cook for 3 minutes. Remove beans from water. Immediately, place in large bowl of icy water to cool and stop cooking process. When beans are cool, remove from water. Place in bowl lined with paper towels. Dry beans well. Add olive oil to beans; toss to coat.
2. For the aioli, chop garlic clove on a cutting board with salt and pepper to make a paste. Add mayonnaise to bowl; stir in garlic paste. Add lemon juice and zest; stir to combine. Refrigerate until ready to serve.
3. Heat large cast-iron skillet over high heat for 2 minutes. Add walnuts. Cook for 30 seconds, stirring continuously. Remove and set aside. Working in 4 batches, add a handful of beans to skillet. Cook until charred and blistered for 2 to 3 minutes, stirring occasionally. Remove and repeat with remaining beans. 
4. When all beans have been cooked, turn off heat. Add all beans back to pan. Add butter, salt and pepper. Toss to coat. Serve with toasted walnuts and a drizzle of aioli.

Calories: 183, Fat: 15 g (3 g Saturated Fat), Cholesterol: 10 mg, Sodium: 255 mg, Carbohydrates: 12 g, Fiber: 3 g, Protein: 3 g.