Whisk yogurt and vegetable oil in a medium bowl. Stir in cilantro and mint, kosher salt, red pepper flakes, and black pepper. Fold in crabmeat and mango.
Thinly spread yogurt on one side of each slice of bread. Divide crab mixture among 8 slices; top with remaining bread, yogurt side down. Trim crusts. Cut each sandwich in half on a diagonal.
Place toasted sesame seeds on a plate, if desired. Dip one cut side of each sandwich in sesame seeds.
Credit: The Bon Appétit Test Kitchen May 2012 - http://www.bonappetit.com/recipe/sesame-crusted-crab-and-mango-tea-sandwiches