Preheat the oven to 350ºF (180°C). Line an 8-inch (20-cm) square baking pan with parchment paper.
Combine the dairy-free butter and chocolate in a large heat-safe bowl.
Bring a small saucepan of water to a simmer over medium heat.
Place the bowl of chocolate and butter on top of the pot of water (the water shouldn't touch the bowl).
Let the steam from the water warm the underside of the bowl (double boiler-style) until the chocolate and butter are melted.
Once the chocolate mixture is melted, turn off the heat. Whisk in the eggs, then add the sugars, baking powder, salt, and vanilla. Whisk again until smooth.
Next, stir in the flour until the mixture is smooth. Add the pecans and stir to combine.
Scoop the mixture into the prepared pan and bake the brownies for 23 to 25 minutes.
Let the brownies cool completely in the pan, then slice to serve. Once cool, store in the fridge.