Preheat the oven to 250 degrees F (120 degrees C). Line a baking sheet with parchment paper.
Beat egg whites and vanilla extract in a large bowl; add almonds and toss to coat. Stir brown sugar, white sugar, cinnamon, and salt into almonds until blended. Spread almond mixture into prepared baking dish.
Bake in the preheated oven, stirring every 15 minutes, until coating is dry, about 1 hour and 15 minutes.