Season the chicken inside and out with salt and pepper.
In a 12 to 14-inch saute pan, heat 4 tablespoons of oil until almost smoking. Add the leeks, liver, and giblets and cook 10 to12 minutes. Remove the leeks and liver to a medium bowl and giblets to a cutting board, chop giblets and add them to the bowl. Add the salami and the cheese, mix well, season with salt and pepper, and stuff the bird with the mixture.
Cut a length of butcher's twine 18 inches long. Secure the wings and legs with the twine and tie the legs together, to seal in the stuffing.
In a Dutch oven, heat the remaining oil over high heat until just smoking. Place the chicken in the pan and brown all sides well, a process that takes about 10 minutes. Add the wine, currants and pine nuts and bring to a boil. Reduce the heat to an active simmer, adding wine when necessary, for 1 hour, turning carefully every 15 minutes. Remove, carefully cut off the string, and carve the chicken into portions.