Preheat the oven to 375°F and move the rack to the center position.
In a small bowl combine the salt, pepper and paprika.
Pat the chickens dry with paper towels and rub the spice mixture under the skin and over the outside of each chicken. Tuck the wings behind the back and tie the legs together with kitchen twine to ensure even cooking without burning of the wings.
Stir the cornstarch and 1 tablespoon of water together in a small bowl until no lumps remain; set aside.
In a small saucepan bring the honey and 4 tablespoons of vinegar to a simmer over medium-high heat. Cook until the mixture is reduced to about 1/2 cup, about 8-10 minutes, stirring occasionally. Slowly whisk the cornstarch mixture into the glaze. Return to a simmer and cook for one minute. Set aside.
Arrange the chickens, breast side down, on a V-rack set inside a roasting pan. Roast until the chickens are golden, about 35 minutes.
Remove the roasting pan from the oven and carefully with a wad of paper towels, flip the chickens so that they are breast side up.
Raise the oven temperature to 450°F . Pour 1 cup water and the broth into the roasting pan. Return the roasting pan to the oven and roast until the thigh meat registers 165 to 170°F, about 35-45 minutes.
Brush the chickens evenly with a thick layer of the glaze and continue to roast until the glaze is golden brown, about 10 minutes.
Transfer the chicken to a cutting board and brush with the remaining glaze and let it rest for 15 minutes to ensure that the juices redistribute and settle.
While the chicken is resting, pour pan juices and any accumulated chicken juices into a saucepan and skim any fat. Stir in the thyme. Bring to a simmer and cook until the sauce is slightly thickened and reduced to 1 cup, about 15 minutes.
Off the heat whisk in the butter and remaining vinegar. Season with salt and pepper. Carve the chickens and serve, passing the sauce at the table.