Preheat the oven to 350°F. Line a 9 x 9-inch baking pan with parchment paper, leaving a little overhang on the sides for easy removal.
In a small bowl, stir together the ground flaxseed and water to make flax-eggs. Set aside for 5 to 10 minutes to thicken slightly.
In a large mixing bowl, whisk together the dry ingredients of flour, cocoa powder, granulated sugar, baking powder, and salt. Stir in chocolate chips.
In another bowl mix together the wet ingredients of the vegan butter, non-dairy milk with ground flax, apple cider vinegar, and vanilla extract. Combine well.
Add the dry ingredients into the wet ingredients. Do not overmix.
Spread the brownie batter evenly into the prepared baking pan. Bake for 15 to 18 minutes, just until the top begins to set but the brownies are not fully baked.
While the brownie layer is baking, make the pecan topping. In a medium bowl, whisk together the brown sugar, maple syrup, plant-based milk, melted vegan butter, cornstarch, vanilla extract, and salt until smooth. Stir in the chopped pecans.
Remove the partially baked brownies from the oven. Carefully spoon the pecan mixture over the brownie layer and gently spread it evenly.
Return the pan to the oven and bake for another 22 to 27 minutes, or until the edges are set and the pecan topping looks glossy and lightly bubbling. The center should be slightly set but not dry.
Let the brownies cool completely in the pan before slicing. For the cleanest slices, chill the brownies for 1 to 2 hours before cutting.
Once cooled, slice the brownies into squares and serve. Enjoy your delicious Vegan Pecan Pie Brownies!