Heat the pot. Set the Instant Pot to Sauté at medium heat, with the lid off. When the display reads HOT, add 1 tablespoon of the butter.
Brown the beef. Add the beef in a thin layer and break it up with a stiff spatula. Cook 8 to 10 minutes, until browned and no pink remains, and a thermometer reads 71°C (160°F). Spoon off fat beyond about 2 tablespoons.
Cook the onion. Push the beef to one side, add the remaining butter and the onion, and cook about 3 minutes, until soft and translucent.
Add the cabbage. Stir in the cabbage and broth. Cook uncovered, stirring often, for 7 to 10 minutes, until the cabbage is soft and the broth has mostly evaporated.
Season. Stir in the garlic, paprika and Italian seasoning and cook 1 minute, until fragrant.
Whisk the eggs. Beat the eggs with the salt and pepper in a bowl until the whites and yolks are fully combined.
Lower the heat. Turn off Sauté, or switch to the lowest setting. The pot is still hot, and the eggs should not sizzle hard when they hit it.
Fold in the eggs. Pour the eggs over the mixture and fold gently with a spatula for 2 to 3 minutes, scraping the bottom, until soft curds form and no liquid egg remains.
Serve. Sprinkle with chives and serve right away, with hot sauce or sour cream if you like.