Preheat oven to 350°F (175°C). Grease a 9x13-inch or Bundt pan.
In a blender, combine carrots, eggs, and oil. Blend until smooth.
Add sugar and pulse to mix.
In a large bowl, whisk flour, baking powder, and salt.
Pour in wet mixture and stir gently until combined.
Pour batter into prepared pan. Bake for 30–40 minutes.
Cool for 15 minutes before glazing.
For the glaze, melt chocolate, butter, and syrup over a double boiler. Add milk if needed.
Pour over warm cake and let set before serving.