Shred the cabbage into thin slices using mandolin or by cutting it in half or into quarters, then finely shredding each piece with the flat end of the cabbage against the counter. Place sliced cabbage into a large mixing bowl. Sprinkle 1 tsp of salt on the cabbage and scrunch the cabbage using both hands for 30 sec to soften it.
Dice the onion and grate both carrots.
Preheat a large skillet or dutch oven over medium-high heat. Add 2 Tbsp of olive oil. Saute onions and carrots for 5 min, mixing frequently. When almost done, mix in 2 Tbsp of sour cream. Empty contents of the skillet into mixing bowl with the cabbage.
Cut pork into small cubes.
Using the same skillet, add 2 Tbsp of olive oil and cook pork for 5 min over medium-high heat, stirring occasionally. When cooked through, add it to the mixing bowl with cabbage, carrots and onion.
Add 1 Tbsp of brown sugar, 1 tsp of salt, 1/2 tsp of pepper, 4 Tbsp of ketchup and mix all contents of the bowl together.
Add 2 Tbsp of olive oil to large skillet or dutch oven. And cabbage mixture and set the heat to medium. Add 2 bay leaves.
Cover and cook cabbage for 35-40 min, stirring every 15 min. Reduce temperature to medium-low after 20 min. Add more ketchup or salt to taste, if desired. Remove bay leaves before serving.
Notes
Cooking time may vary - if not using a dutch oven, you may need to add an extra 5 minutes if cabbage is not soft enough.