Preheat the oven to 350 degrees F (175 degrees C).

Mix 1/4 cup butter, garlic, paprika, Italian seasoning, herb seasoning, salt, and pepper together in a bowl.

Place turkey, skin-side up, in a roasting pan. Loosen skin with fingers; spread 1/2 of the butter mixture over turkey and under skin. Reserve remaining butter mixture. Tent turkey loosely with aluminum foil.

Bake in the preheated oven for 1 hour. Baste with remaining butter mixture, return to oven and continue to cook until juices run clear and an instant-read thermometer inserted into the thickest part of the breast reads 165 degrees F (74 degrees C), about 30 minutes more. Remove to a cutting board and let rest for 10 to 15 minutes.

Transfer about 1 tablespoon of pan drippings to a medium skillet. Add shallot and cook on low until translucent, about 5 minutes.

Add 1 tablespoon butter to the skillet; whisk in wine, scraping up any browned bits from the bottom of the pan. Whisk in stock and flour until smooth. Bring to a simmer, whisking constantly, until thickened. For a creamier, lighter gravy, whisk in half-and-half.

Slice turkey and serve with gravy.