In a large sauce pan, bring the cranberries, sugar and 1/2 cup water to a boil over high heat. Reduce the heat to medium and cook, stirring occasionally, until the cranberries pop and the sauce thickens, about 15 minutes. Turn off heat and cover the sauce to keep it warm while you make the burgers.
In a medium bowl, combine the ground turkey, chopped scallions and Worcestershire sauce. Season with salt and pepper; gently mix in the blue cheese. Form into 4 large parties (thinner in the centers for even cooking).