Heat pecans in a small nonstick skillet over medium-low heat, stirring often, 8 to 10 minutes or until toasted and fragrant.
Combine ground turkey, next 3 ingredients, and pecans in a large bowl. Shape into 6 (1/2-inch-thick) patties, shaped to fit bread slices.
Cook patties in a large lightly greased skillet over medium heat 5 to 6 minutes on each side or until done.
Stir together cranberry sauce and Dijon mustard. Spread 1 Tbsp. cranberry mixture on 1 side of each bread slice. Layer 6 sourdough bread slices with Monterey Jack cheese, arugula, and turkey burgers; top with remaining bread slices, cranberry mixture side down.
Cook sandwiches, in 2 batches, on a hot griddle or in a lightly greased skillet over medium heat 2 to 3 minutes on each side or until golden brown and cheese melts.