Optional for serving: fried egg, or a dollop of sour cream or plain Greek yogurt
In a large skillet, heat 1 tablespoon of olive oil and add the chopped onion. Saute for 2-3 minutes, or until the onion starts to soften and turn golden brown.
Add the sliced cabbage, 1 teaspoon salt, and diced parsley. Cover with a lid and saute for 10-15 minutes over medium heat, stirring occasionally.
Combine all the ingredients in a large bowl - sauteed cabbage, mashed potato, eggs, 1 cup flour, the remaining teaspoon salt, and pepper.
Mix the ingredients. Add more flour if the mixture is not a thick paste (see notes). Use an ice cream scoop to scoop out about 1/4 cup of the potato cabbage mixture.
Place the scoop of potato cabbage mixture on a plate with flour for dredging. Roll the mixture around in the flour, then press down gently to form a patty.
Heat 1 tablespoon of olive oil in a large skillet. Carefully place the bubble and squeak patties on the hot oiled skillet and cook for 3-4 minutes over medium heat, or until golden brown. Flip carefully and cook on the other side for 3-4 minutes.
Repeat step 6 until all the bubble and squeak cakes are cooked. Serve warm with a fried egg and a dollop of sour cream or plain Greek yogurt.
The potato and cabbage mixture should be the consistency of paste. It should be able to be formed into a soft patty without falling apart. If your patties are falling apart, stir in more flour. Try not to overdo it on the flour or the bubble and squeak cakes will be tough
You can use the same skillet for cooking the cabbage and frying the bubble and squeak cakes. Just wipe it down with a paper towel after the cabbage
Other additions to try:
Shredded cheese (cheddar, Parmesan, etc)
More fresh herbs (parsley, tarragon, scallions, chives)
Crumbled bacon (cook it first, then saute the onion and cabbage in bacon grease)