Preheat the oven to 350°F. Coat an 8x8-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, 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. Pour the batter into the pan and bake 35 to 40 minutes. Cool completely in the pan before cutting into 12 bars.
For the carrots: Peel, trim the ends, and cut into 3-inch chunks. Steam for 10 to 12 minutes until very tender. Puree in a food processor or blender for about 2 minutes until smooth, adding a few teaspoons of water, if needed, for a smooth texture.
For the spinach, remove any tough stems. Steam for 30 or 40 seconds, or cook in a skillet with 1 tablespoon water for about 90 seconds until wilted. Puree in a food processor or blender for about 2 minutes until smooth and creamy.