Melt butter in a large skillet over medium heat. Cook and stir cabbage and onion in the butter until the vegetables are very tender and dark brown, 25 to 30 minutes.
Whisk eggs, matzo meal, cider vinegar, sugar, salt, and black pepper in a large bowl; allow mixture to rest for about 3 minutes.
Stir cabbage mixture into egg mixture until well mixed; pour mixture into prepared baking dish.
Bake kugel in the preheated oven until browned, about 30 minutes.
