Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 13×9-inch baking pan.
Sift together flour, baking powder, and salt in a bowl.
Blend oil, sugar, eggs, and carrots in a blender, stopping to scrape down sides, until creamy and smooth, about 1 minute. Pour puree into a large bowl, then whisk in flour mixture until combined. Pour batter into prepared pan.
Bake in preheated oven until a toothpick inserted into center comes out clean, about 40 minutes. Transfer pan to a rack to cool, about 1 hour.
Stir together milk, chocolate, honey, and butter in a heavy saucepan and bring to a boil over medium heat, stirring. Reduce heat to medium-low and simmer, stirring constantly, until mixture is smooth, thick, and reduced to about 1 1/8 cups, about 10 minutes.
Pour frosting into a metal bowl and set in a larger bowl of ice water. Stir frosting until cooled and thickened, about 5 minutes. Frost cake evenly and cut into 12 pieces to serve.
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