Grease the slow cooker bowl with vegetable oil. Grate the carrot, finely chop the onion and add them to the bowl. Add salt, sugar and spices, close the lid and saute for 5 minutes on the "fry" setting.

While the vegetables saute, shred the cabbage and gently squeeze it with your hands to soften it. Add the cabbage to the bowl and cook for another 15 minutes on the same setting.

For the batter, whisk the eggs with sugar, salt and vanilla into a fluffy foam. Add the sour cream and grated cheese, and mix. Finally, stir in the flour - the batter should have a pancake-like consistency.

Open the slow cooker and pour the batter over the cooked cabbage. Close the lid and bake for 40-45 minutes on the "bake" setting.

Let the finished pie cool completely in the bowl, then remove it using the steamer rack. Cut into pieces and serve. Enjoy your meal!