How to Make It
Melt butter in a large skillet over medium-high. Add onion, celery, and garlic; cook, stirring occasionally, until vegetables are slightly soft, 3 to 4 minutes.Stir in sage and rosemary; cook 1 minute. Transfer to a plate; cool completely, 8 to 10 minutes.
Combine onion mixture, turkey, salt, and pepper. Form into 4 (5-ounce, 1/2- inch-thick) patties.
Preheat broiler to high. Heat oil in a large nonstick skillet over medium-high. Add burgers; cook until golden brown, 3 to 4 minutes per side. Top burgers with cheese slices. Broil until a thermometer inserted in thickest portion of burger registers 160°F, about 1 minute.
Stir together cranberry sauce and mayonnaise, and divide among top halves of buns. Spread 2 teaspoons mustard on bottom half of each bun. Top with burgers, green beans, fried onions, and top halves of buns.