½ cup mayonnaise
1 tablespoon lemon zest (from 1 large lemon)
3 garlic cloves, grated
Kosher salt (Diamond Crystal) and black pepper
1 tablespoon smoked paprika
1 teaspoon chopped rosemary leaves (or ½ teaspoon dried rosemary)
½ teaspoon red-pepper flakes
2 large bone-in, skin-on chicken breasts (1½ to 2 pounds total), patted dry
1 large russet potato (about 1 pound), scrubbed
1 tablespoon olive oil
1 tablespoon lemon juice
Heat the oven to 425 degrees, and place a sheet pan on the oven’s lowest rack to heat. In a liquid measuring cup or small bowl, stir together the mayonnaise, lemon zest and garlic. Season with salt and pepper.
Transfer half of the mayonnaise mixture (about ¼ cup) to a medium bowl. Stir in the smoked paprika, rosemary, red-pepper flakes and ½ teaspoon black pepper. Season the chicken all over with 1½ teaspoons salt. Add the chicken to the bowl of paprika-mayonnaise, and rub it all over the chicken. Set aside.
Halve the potato crosswise (no need to peel), then cut it into ¼-inch-thick fries. Right on the cutting board, drizzle with the olive oil, and season with salt and pepper. Toss to coat.
Place the chicken breasts skin side down on the heated sheet pan, then scatter the potatoes around the chicken in a single layer. Roast on the bottom rack for 15 minutes, then flip the chicken so the skin side is up. (No need to turn the potatoes.) Roast for another 10 to 15 minutes, until the fries are browned underneath and the chicken registers 155 degrees when an instant-read thermometer is inserted in the thickest part. (The temperature will rise as the meat rests.) Let the chicken rest for at least 5 minutes, then cut the chicken meat from the bones and slice. Stir the lemon juice into the remaining mayonnaise mixture. Eat the chicken with the fries and a puddle of the lemon-garlic mayo for dipping.