Using the flat side of a knife blade, mash the garlic and 1/2 teaspoon of salt together into a paste. Rinse and pat the chicken dry, inside and out, and put the chicken on a plate. Rub the chicken all over with the lemon quarters.
Slip your fingers underneath the skin to loosen it. Slide the garlic paste between the skin and chicken, being careful not to tear the skin. Then smooth the skin to evenly distribute the paste.
In a small bowl, whisk together the vinegar, 2 tablespoons of wine, the oil, paprika, cumin, black pepper, and oregano.
Place the chicken in a baking dish and slather it with the marinade. Turn the bird several times to coat. Cover and refrigerate for 5 to 8 hours, turning the chicken once or twice. Preheat the oven to 425ºF (220°C). Adjust the oven rack to the middle position.
Move the chicken to a small roasting pan or 12- to 14-inch cast-iron skillet. Don't toss out the marinade.
Squeeze the lemon quarters into the cavity of the hen and then toss them in. If desired, tie the legs together with kitchen string. Season the chicken all over with 1 teaspoon salt.
Roast the bird for 15 minutes. Reduce the heat to 375ºF (190°C). Dump the marinade over the bird and roast, basting occasionally with the pan juices, until an instant-read thermometer inserted in the thigh reads 165ºF (74°C), about 75 minutes more.