Thoroughly clean carrots and slice off the top and very tip. Place them onto a level cutting board.
Place the tip of a sharp knife on the cutting board with the entire carrot beneath it. Lever the knife down through the carrot and back up to make thin Hasselback cuts. Do not cut all the whole way through to the board, stop after ¾ of the way. Repeat down the length of the carrot.
Blanch carrots in a pot of salted boiling water on the stovetop for 3 minutes then drain and allow to dry completely.
Preheat oven to 180C/355F.
Move the carrots into an oven dish in a single layer.
Melt the butter and pour it over the carrots, using a pastry brush to get it into the slits in the carrots. Sprinkle over the rosemary and season with salt and pepper.
Roast the carrots for 25 minutes, then baste again with the butter and brush honey over the surface. Return to the oven for a further 10-15 minutes until cooked.