8 boneless, skinless chicken breast cutlets (about 2 pounds total)
1 1/4 teaspoons freshly ground black pepper, divided
12 small fresh sage leaves, divided
8 thin slices prosciutto (about 6 ounces)
1 pound baby new potatoes, sliced in half lengthwise, quartered if large
1 garlic clove, finely chopped
3 tablespoons olive oil, divided
3/4 teaspoon kosher salt, divided
3 oil-packed anchovy fillets, drained, finely chopped
1 tablespoon red wine vinegar
2 teaspoons honey
1 bunch curly kale (about 8 ounces), ribs and stems removed, coarsely chopped

Position racks in upper and lower thirds of oven and preheat to 425°F. Arrange chicken cutlets in a single layer on rimmed baking sheet and season with 1/2 tsp. pepper. Place 1 sage leaf on top of each cutlet, then wrap each in 1 slice of prosciutto, starting from the top and wrapping in a single layer, making sure cutlet stays flat. Finely chop remaining 4 sage leaves and toss with potatoes, garlic, 1 T. oil, 1/2 tsp. salt, and 1/2 tsp. pepper on second rimmed baking sheet. Cook chicken in upper third of oven and potatoes in lower third until prosciutto is crisp and an instant-read thermometer inserted into the thickest part of chicken registers 165°F, 12-14 minutes. Meanwhile, whisk anchovies, vinegar, honey, and remaining 2 T. oil, 1/4 tsp. salt, and 1/4 tsp. pepper in a large bowl; add kale and toss to coat. Remove both baking sheets from oven; let chicken rest. Spread kale evenly over potatoes and return to upper third of oven. Roast until potatoes are tender and kale is browned at edges, about 5 minutes more. Divide chicken among 4 plates. Serve potatoes and kale alongside.