Chop the carrot into pieces of roughly the same size.
Add the carrot pieces, sugar and a pinch of salt to a pan, and cover with water.
Bring to a boil, and let reduce until the carrot is cooked, and the sugar is starting to caramelize. 15-20 minutes.
While everything else is boiling, roughly chop the garlic and ginger, and add it to the bowl of a food processor along with the Kimchi.
Deglaze the pan with the carrots with some boiling water, and then pour everything into the food processor, and blitz until puréed.
Return to the pan on low to keep warm, and add salt to taste.
Mix the gochujang/honey together, adding some hot water if needed to loosen it.
Place the salmon on a baking sheet, and coat the tops with the gochujang/honey mixture.
Bake at 180°C until cooked. In my case this was just under 20 minutes.
Serve atop the Kimchi/Carrot puree with some pickled vegetables, and a side of plain white rice.