Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Stir stuffing mix, soy milk, sage, and salt together in a bowl; add turkey and stir until thoroughly combined. Divide turkey mixture into 4 equal portions and shape into 1/2-inch thick patties. Place patties on a broiler pan.
Cook turkey burgers in the preheated broiler until no longer pink in the center and juices run clear, about 6 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Toast hamburger buns in a toaster.
Arrange lettuce leaves on bottom halves of hamburger buns. Place turkey patties and cranberry sauce on top of lettuce and place top half of bun on top.