Bring water and kasha to a boil. Reduce heat to low and simmer, without stirring, until kasha groats are soft and fully open, about 15 minutes. Let cool.

Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

Stir carrots, parsley, olive oil, basil, thyme, oregano, paprika, mustard, and cayenne pepper into the kasha. Form mixture into patties and place on the prepared baking sheet.

Bake in the preheated oven until browned on the outside, about 30 minutes.