Puntarelle, a bitter green, makes a soft blanket for delicately fried (but not greasy) chicken. The anchovy-and-garlic emulsion is a classic Italian dressing.
Make the salad: Toss together puntarelle, basil, and scallions in a large bowl.
Mash garlic and a pinch of coarse salt into a paste usinga mortar and pestle or scrape into a paste using the sharp side of a knife. Add anchovies, and mash. Transfer mixture toa small bowl, and stir in lemon juice. Gradually add oil, whisking constantly, until emulsified.
Make the chicken: Combine buttermilk, eggs, baking powder, and baking soda in a medium bowl. Whisk together flour, 1 tablespoon coarse salt, and some pepper in another medium bowl.
Fill a medium pot halfway with oil. Heat oil over medium heat until it reaches 380 degrees on a deep-fry thermometer. Dip each piece of chicken into buttermilk mixture to coat, shaking off excess. Dredge each piece in flour mixture to coat, patting it onto chicken as you work, making sure each piece is heavily coated.
Working in batches, carefully fry chicken until deep golden brown, about 3 minutes. Drain on paper-towel-lined plates. Sprinkle with sea salt.
Toss salad with half the dressing. Season with coarse salt and pepper. Divide 3 or 4 fried chicken strips among 6 plates, and top with salad. Garnish with lemon wedges, and serve with remaining dressing on the side.