Preheat oven to 425°F with a rack in the center. Choose a roasting pan that will accommodate the chicken and potatoes. (A good old 13" x 9" metal roasting pan that's on the deeper side and safe for the stovetop usually works well.)

Place the chicken in the pan breast-side up and slide your fingers gently between the skin and the breast to make a pocket on each side.

In a small bowl, mash together the butter, chopped prosciutto, garlic, sage, lemon zest, and pepper.

Use your hands to spread most of the butter mixture between the skin and breast of the chicken, then rub the rest all over the outside of the bird.

Tuck the thyme sprigs and lemon halves into the cavity of the chicken.

Roast for 20 minutes.

Use tongs to lift up the chicken for a moment and add the diced potatoes to the bottom of the roasting pan.

Roast for 40+ minutes more, until an instant thermometer inserted into the thickest part of the thigh (but not touching the bone) reads 165°F.

Let chicken rest on carving board for 15 minutes. If potatoes are done to your liking, spoon them into a serving bowl. If not, return to oven while chicken rests.

If making gravy: Set roasting pan over medium-high heat on the stove (one or two burners, depending on the size of your pan).

Whisk flour into pan drippings and let brown for a minute. Then whisk in wine and simmer for a minute or two. Pour in stock, whisk to remove any lumps, and simmer for 5 to 10 minutes until nicely thickened.

Carve chicken and serve with potatoes and gravy to pass at the table.