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Make the compound butter: Place all ingredients in a medium bowl and stir with a small spatula to combine evenly. Taste and adjust seasonings if needed.
Pat the turkey breast dry with paper towels and season all over with salt and pepper. Rub half of the compound butter underneath the skin of the turkey breast and the remaining half of butter all over the outside, including the bottom and sides.
Place a wire rack inside a clean roasting pan. Set the turkey breast skin side up in the pan and place on the center rack of the oven. Baste every 15 minutes with the fat rendered in the pan. About halfway through into roasting, carefully pour the ½ cup stock into the pan so the juices do not burn. Roast for 45-55 minutes total, until cooked through and skin is crisp and golden and the juices run clear. An internal thermometer should register at least 155°F (68°C), keeping in mind that cooking will carry over and continue as it rests.
Let the breast rest on a cutting board while you make the gravy, and tent with foil if desired.
Carefully pour all the pan drippings into a glass jar or heat-proof measuring cup, let sit for a few minutes to settle and separate. Spoon off 1 tablespoon of fat that separated to the top and transfer to a small saucepan. Heat over medium for a moment and add flour, stirring to form a roux. This will make a thick paste. Let this paste cook for a minute before slowly pouring in chicken stock, whisking to incorporate smoothly. Discard any remaining fat from the pan juices and whisk the remaining juice into the gravy.
Let the gravy cook, lowering the heat to simmer if needed, whisking frequently, for about 3-4 minutes until thickened. Season with salt and pepper to taste, if needed.
Remove the gravy from the heat while you slice the turkey. Serve immediately.
Recipe can easily be doubled to serve 4 guests by buying two separate breasts, or even one whole double-breasted turkey (without the wings and legs).
If using bone-in turkey breast, simply add another 15-20 minutes to the cook time.
If a roasting pan with a rack is unavailable, cook the turkey on a wire rack placed over a rimmed baking sheet. Use extra caution when removing the tray from the oven as the juices will be extremely hot.
When selecting a turkey breast, look for skin that has minimal tears and covers as much of the meat as possible.