Preheat the oven to 400 degrees F (200 degrees C). Grease 6 jumbo muffin cups with cooking spray or line with paper liners.

Beat eggs in a large bowl with an electric mixer, gradually adding sugar, until thick and lemon-colored. Mix in sour cream, applesauce, and almond extract.

Combine flour, whole wheat flour, salt, and baking soda in a separate bowl. Stir into the creamed mixture just until dry ingredients are moist. Mixture will be lumpy; do not overmix! Gently fold in blueberries.

Spoon batter into the prepared jumbo muffin cups. Sprinkle whiskey barrel smoked sugar over the top of each muffin.

Bake in the preheated oven until tops spring back when lightly pressed, about 28 minutes. Cool in the cups for 5 minutes. Transfer to a wire rack to cool completely.