Preheat the oven to 350°F. Grease an 8-inch square baking pan with vegan butter and line it with parchment paper, leaving some paper overhanging the sides.
In a large bowl, whisk together the melted butter and sugar until the mixture looks like wet sand.
Add the flaxseed eggs, almond milk, and vanilla extract to the butter and sugar mixture and whisk to combine, then whisk in the sweet potato puree until combined.
In a medium-size bowl, whisk together the flour, cacao powder, baking powder, and salt, then add the dry ingredients to the bowl with the wet ingredients and stir with a rubber spatula or wooden spoon until fully combined. The batter will be very thick and stiff.
Gently fold in half of the chocolate chips and half of the toasted pecans.
Scrape the batter into the prepared baking pan and spread it out evenly. Top with the remaining chocolate chips and pecans and gently press them into the batter.
Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out mostly clean. Remove from the oven and let cool in the pan for 20 minutes, then lift the brownie out of the pan and transfer to a cooling rack to finish cooling.
Once completely cool, slice into 8 squares and serve. Store leftover brownies in a tightly sealed container for up to 3 days at room temperature or refrigerate for up to 5 days. To freeze, wrap the brownies tightly in plastic wrap followed by foil and freeze for up to 3 months. Shortly before serving, thaw at room temperature.