Preheat the oven to 350 degrees Fahrenheit.
In a small bowl, whisk together the 2 tbsp ground flax with 5 tbsp water. Set aside to thicken. Skip this step if using the apple sauce. Some people notice a flavor when using the flax (I never have this issue) so if that worries you, stick to the applesauce. The texture will be slightly different, but still delicious.
In a medium pot on the stove, add the sugar and water and whisk together. Heat over medium/low heat. Stir occasionally, but after about 5-10 minutes, the sugar should completely dissolve. Be sure you don't add any extra water. The water will look somewhat cloudy, but you shouldn't notice any clumps of sugar. This is key for the shiny crust!
Meanwhile, in a large bowl, stir together all dry ingredients except for the chocolate chips if using (we'll add these later). Be sure to spoon and level the cocoa and flour into dry measuring cups, don't scoop right from the bag or you will inadvertently end up with more flour than needed.
Once the sugar has completely dissolved, give it a final whisk, then pour it into the dry ingredients.
Add all remaining wet ingredients, including the flax eggs once thickened or the applesauce and mix together with a wooden spoon until a batter forms. Careful not to over mix, stir just until combined.
Fold in the chocolate chips if using. They're optional, but they do help the top get shinier and add a richer chocolate flavor.
Transfer to an 8x8 baking dish lined with parchment paper.
Sprinkle with additional chocolate chips if desired.
Bake for 35-42 minutes. about 38 was perfect in my oven, but check with a toothpick. Bake for longer if you don't like a fudgy inside and shorter if you want them really fudgy.
Remove from the oven, let cool completely, then slice around the edges of the pan and lift out the brownies using the parchment paper. Slice into 16 squares & enjoy! The longer you let cool, the easier/cleaner the cut will be.