In a medium-sized bowl, use a fork to combine the beef and the egg.Mix the paste with the Curry paste and add salt to taste. Optional: Cover the mixture with plastic wrap and refrigerate for at least 1 hour (Marinating overnight is even better to help the flavors marry.) Brush the patties with butter and grill each side on a pan. Cook the patties to medium-rare or medium doneness, about 3 minutes on the first side, then 4 to 5 minutes on the second side. While the burgers rest, halve the burger buns, and put them, cut side down, on the grill grates. Toast until they are a light golden brown, about 10 seconds. Set aside. To serve, apply some butter onto each side of the bun and a slice of cheese on top of the burger bun. Cover with the top of the buns and serve immediately.