Place couscous in a large bowl. Pour in boiling water, stir and set aside until the water is absorbed, about 5 minutes. If grilling the burgers, preheat grill to medium-high.
Meanwhile, heat oil in a large skillet over medium heat. Add onion and cook, stirring, for 1 minute. Add celery; cook, stirring, until softened, about 3 minutes. Add thyme, sage, salt and pepper; cook until fragrant, about 20 seconds more. Transfer the mixture to the bowl with the couscous, add cranberries and stir to combine. Let cool for 5 minutes. Add turkey and stir until combined; do not overmix. Form the mixture into 6 patties.
To cook on the stovetop: Coat a large nonstick skillet, preferably cast-iron, with cooking spray and set over medium-high heat for 2 minutes. Add the patties, reduce heat to medium, and cook for 4 minutes. Turn and cook on the other side for 2 minutes. Cover and continue to cook until lightly browned but still juicy (the juices should run clear, not pink), about 4 minutes more. (An instant-read thermometer inserted in the center should read 165° F.) To grill: Oil the grill rack (see Tip) and grill the burgers for 5 to 6 minutes per side, flipping gently to avoid breaking them. Serve immediately.