Preheat oven to 350 degrees. Lightly oil a 9-inch square baking pan, then line bottom and sides with parchment and lightly oil parchment.
Toast almonds in a rimmed pan until pale golden, 6 to 9 minutes. Stir in sesame seeds and bake until seeds are golden, 3 to 4 minutes more. Transfer to a plate and cool completely. Reduce oven to 325°F.
Gently heat honey, brown sugar, and oil in a small saucepan over low heat, stirring, until smooth.
Stir together rice cereal, cashews, and almond-sesame mixture in a large bowl. Beat egg whites with a rounded 1/4 teaspoon salt in a small bowl with a fork until foamy, 1 to 2 minutes. Stir honey mixture into cereal mixture, then stir in whites. Spread mixture in baking pan, pressing gently, and bake until golden brown, 35 to 40 minutes. Cool completely, then turn out onto a cutting board and cut into bars.
Created by Chef Libby from Elevation Corporate Health.