Position oven rack in lower third of oven; preheat to 350 degrees F.
Remove giblets. Place hearts, necks and gizzards in roasting pan and reserve
livers for another use.
With a sharp knife, remove excess fat.
Dry insides with a paper towel.
With your fingers, loosen skin over breasts and thighs to make pockets,
being careful not to tear the skin.
In a food processor or blender, combine onion, garlic, paprika, 2 teaspoons
salt and 1 teaspoon pepper; puree until smooth.
Spread 1/4 cup onion puree in the bottom of a roasting pan.
Place chickens in pan, at least 1 inch apart.
Rub 1 tablespoon puree into each cavity and spread remaining puree under
Tuck wings back and tie legs.
Roast chickens for 20 minutes.
Drizzle with 1/4 cup chicken broth and roast for 40 minutes more, basting
with pan drippings every 20 minutes.
Tent chickens with aluminum foil and continue roasting for 30 minutes, or
until an instant-read thermometer inserted into the thickest part of the thigh,
away from the bone, registers 180 degrees F and the cavity juices run clear.
Transfer chickens to a platter and cover with foil to keep warm; leave giblets
Pour pan juices into a bowl and chill in freezer for 10 minutes to bring
fat to the surface.
Meanwhile, add remaining chicken broth and vodka to roasting pan and bring
to a boil over medium heat, scraping up any browned bits adhering to the pan.
Add any juices accumulated on chicken platter.
Skim off fat from chilled pan juices.
Add juices to roasting pan and return to a boil. Strain juices through a
fine sieve into a medium saucepan.
Bring to a simmer over medium heat.
In a small bowl, blend water and cornstarch; whisk into simmering gravy.
Cook, stirring, until slightly thickened, about 1 minute.