Wash the beans and remove the stems. Wash the hakurei turnips and chop into ¼” slices. Heat a cast-iron skillet over medium-high heat. In a large mixing bowl, combine the green beans, turnips and two tablespoons olive oil. Season with salt and pepper and toss well to combine. Add the vegetables to the hot cast iron pan and let sear for 3-4 minutes without moving. Toss to turn once time to sear the other side, for another 3-4 minutes. Once the beans are charred and crisp-tender, remove from the vegetables from the pan and place in a large mixing bowl.
Chop the garlic very finely and mash into a paste using the side of a large chef’s knife.
Add the aquafaba, vinegar, mustard and salt to a bowl and blitz for a second with an immersion blender so everything is combined. Keep the immersion blender running constantly and very slowly drizzle in the oil, making sure it is fully combined as you go. If you add it too fast, the whole thing will turn liquidy and isn't redeemable. Once all the oil is combined and thoroughly mixed. Add in the lemon juice and garlic and mix thoroughly. Season with salt and pepper to taste. Toss the beans and turnips with the aioli, then garnish with fresh herbs and pecans if you have on hand.