Combine ground flax seed and 5 tablespoons of water in a small bowl, stirring well to combine. Set aside for 5 minutes to allow the mixture to thicken into a gel-like consistency—this will act as your egg binder. While waiting, preheat your oven to 350°F and prepare a 9x13 inch baking dish by lightly oiling it or lining it with parchment paper.

In a small saucepan, combine 1 3/4 cups sugar with 1/2 cup water over medium heat. Stir occasionally and let it simmer for 5-10 minutes until the sugar is completely dissolved and the mixture becomes syrupy. This concentrated sugar syrup will replace the moisture that applesauce would normally provide, creating moisture and sweetness throughout the brownies. Remove from heat and set aside to cool slightly.

In a large mixing bowl, whisk together the cocoa powder, all-purpose flour, salt, and espresso powder. I like to sift the cocoa powder first to remove any lumps—it ensures a smoother, lump-free batter with better chocolate distribution. Make sure to break up any clumps as you combine these dry ingredients; a well-mixed dry mixture prevents streaking in the final batter.

Pour the cooled sugar syrup from Step 2 into the dry ingredient mixture from Step 3, stirring gently to begin combining. Add the oil, vanilla extract, and the thickened flax mixture from Step 1. Stir everything together until you have a smooth, cohesive batter with no visible streaks of dry ingredients. The batter should be thick but pourable—don't overmix, as this can make the brownies tough.

Gently fold the chocolate chips into the batter using a spatula or wooden spoon, being careful not to overmix. Pour the batter into your prepared 9x13 inch baking dish, spreading it evenly with the back of a spatula. For extra fudgy brownies, I actually slightly underfill and spread the batter a bit thinner—it creates those perfect chewy edges and a more cake-like crumb structure.

Bake in the preheated 350°F oven for 35-42 minutes, checking at the 35-minute mark. The brownies are done when a toothpick inserted in the center comes out with just a few moist crumbs—they should not look wet or raw, but slight moistness is perfect for fudginess. Remove from the oven and allow the brownies to cool in the pan for at least 15-20 minutes before slicing; this helps them set up and makes for cleaner cuts.