Preheat oven to 300. Place a wire rack on a baking sheet and set aside. Heat 1 tsp canola oil in a large skillet over medium heat. Beat eggs with 2 tbs water in a shallow baking dish. Dip 2 slices bread in egg mixture and flip to coat. Swirl oil to coat skillet. Transfer bread to skillet, allowing excess egg to drip into baking dish first, and cook until undersides are golden brown, 1 to 3 minutes. Flip and spread with honey mustard (about 1 1/2 ts per slice), then top 1 slice with a quarter of the turkey, arugula and cheese. Cook until undersides are golden brown and cheese begins to melt, 1 to 2 minutes, then top loaded slice with second slice, mustard side down. Transfer sandwich to rack and place in oven. Reduce stovetop heat
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