Heat the oven to 180°C/350°F.
Mix the ricotta, lemon zest, sage, salt, and pepper.
Lay out the prosciutto, place a chicken thigh near the bottom of each strip, and divide the ricotta filling between them.
Roll each chicken piece in prosciutto, finishing seam-side down; secure the ends with toothpicks if needed.
Fan the potato slices in a roasting dish or large ovenproof skillet. Mix 1 1/2 tablespoons oil with garlic and spread it over the potatoes; season with salt, pepper, and thyme.
Set the chicken over the potatoes, drizzle with the remaining oil, and bake for 40 minutes.
Rest the chicken loosely covered with foil. Sprinkle Parmesan over the potatoes, return them to the oven, raise the heat to maximum, and bake for 5 minutes.
Remove the potatoes, put the chicken back on top, and serve promptly.