1/4 cup unsalted butter
2 large yellow onions (about 10 ounces each), finely chopped
2 English muffins
3/4 cup cold water
3 large eggs
2 tablespoons ketchup, plus more for glazing
1 tablespoon kosher salt, plus more to taste
1 teaspoon freshly ground black pepper
2 pounds ground beef (preferably 15 to 20% fat)