Preheat the oven to 350°F. Coat an 8×8-inch baking pan with cooking spray.
Melt the chocolate in a double boiler or over a very low flame.
In a large bowl, combine the melted chocolate, vegetable purees, sugar, cocoa powder, flax margarine, and vanilla, and whisk until smooth and creamy, 1 to 2 minutes.
Whisk in egg whites. Stir in the flour, baking powder, and salt with a wooden spoon. Then stir in the milk, then the walnuts.
Pour the batter into the pan and bake 35 to 40 minutes. Cool completely in the pan before cutting into 12 bars.