Preheat the oven to 350°F (175°C or 165° for fan ovens, gas mark 4).
Lightly grease a 9 x 9 x 1¾ inch (23 x 23 x 5 cm) square baking pan.
Heat the butter and chocolate together in a saucepan over very low heat, stirring constantly, until the two ingredients melt together.
Remove the pan from the heat and stir in the sugar, applesauce and vanilla. Then stir in the beaten eggs.
Sift together the flour, cocoa, baking powder, baking soda and salt together and stir into the mixture in the saucepan.
Beat with a wooden spoon until smooth, then stir in the chopped pecans.
Spread the batter in the pan, smoothing the top.
Bake for 15 to 20 minutes, or until the top springs back when touched lightly.
Cool completely (or for as long as you can resist) before cutting and serving. The brownies do slice better the closer they are to room temperature.