1. Preheat oven to 250°. Brush a rimmed baking sheet with oil.
2. In a large bowl, using your hands, mix walnuts, oats, pecans, almonds, sunflower seeds, coconut, cinnamon and nutmeg.
3. In a medium bowl, gently beat egg whites and maple syrup with a fork, taking care to keep foam to a minimum. Pour egg white mixture over dry ingredients and mix thoroughly with your hands to evenly coat.
4. Transfer mixture to baking sheet, spreading it out so that it’s slightly thicker toward sides. (This will prevent granola at edges from sticking during baking.) Bake granola mixture for about 25 minutes, then rotate baking sheet and bake for 25 minutes longer. Remove baking sheet from oven, carefully mix granola with a spatula and continue to bake until golden brown, 25 to 30 minutes.
5. Let cool on a wire rack, then transfer to a large bowl. Add dried blueberries, apricots and dates and mix thoroughly to combine. The granola can be stored in an airtight container for up to 2 weeks.