Place 1 1/4 cups of carrot juice, carrots, butter, honey, and curry powder in a saucepan over medium heat. Bring to a simmer. Reduce heat to medium-low and simmer until liquid is evaporated and carrots are very soft, about 1 hour.
Add heavy cream and increase heat to medium and bring to a simmer. Simmer for 3 minutes.
Place cream and carrots in a blender. Add remaining 1 1/4 cups of carrot juice and blend on high until smooth.
Taste and season with salt and pepper, blending to incorporate between additions.
Strain through a fine mesh strainer into a non-reactive bowl. Refrigerate and chill completely.