Butterfly the chicken: Rinse chicken and pat dry with paper towels. Butterfly the chicken by using poultry shears or a knife to cut along one side of the backbone.
Cut along the other side and remove the backbone and tail. (See our guide to how to spatchcock or butterfly a chicken.)
Spread the chicken open, skin side up. Press down on the chicken with the palms of your hands (or pound with your fists) to flatten the chicken. Fold the wings under the chicken.
Make ricotta Parmesan herb mixture: In a medium bowl, mix the ricotta, Parmesan cheese, egg, parsley, garlic, 2 teaspoons of chopped basil, and 1 teaspoon of chopped tarragon.
Stuff ricotta mixture under chicken skin: Using a sharp paring knife and your fingers, loosen skin over top of chicken and drumsticks starting at neck edge. Work with your fingers and hand to press under the chicken skin to separate the chicken skin from the chicken breasts, thighs, and drumsticks. Be gentle, the skin can easily tear.
Carefully spoon cheese mixture under skin of chicken, pressing with your fingers to distribute evenly over the chicken and drumsticks.
Brush chicken lightly with oil; sprinkle with 1/2 teaspoon basil, 1/2 teaspoon tarragon, paprika, and a generous amount of salt.
chicken using an oven: Preheat oven to 500°F.
Place chicken, skin side up, on a rack in a roasting pan.
Place in oven and immediately turn the heat down to 350°F.
OR Cook chicken using a grill: Prepare grill for medium indirect heat. If using a gas grill, heat all burners on high until the grill is hot, then turn off the middle burner.
If using a charcoal grill, bank the coals to one side of the grill and place a large aluminum drip pan underneath the grate on the side without coals, adding a couple cups of water to the drip pan so that the drippings don't burn.
Place the chicken, skin side up, on the cooking grate, away from the side with coals if you are using a charcoal grill, or above the middle burner if you are using gas.
Alternatively, you can lay the chicken out on a rack in a disposable aluminum roasting pan and place the roasting pan on the cooking grate (this tip works well with gas grills, I haven't tried it with the charcoal one yet). Cover the grill.
Roast the chicken for an hour or until the juices run clear from the thigh when pierced with a fork. (Chicken should have an internal temperature of 165°F when tested with a meat thermometer.) If the skin browns before the chicken is cooked through, cover it loosely with foil.
Transfer chicken to a cutting board; let stand 10 minutes.
