Spread a thin and even layer of butter on one side of each slice of bread.
Take four bread slices, butter the other side (so that both sides are buttered), and spread one side with thin layer of the chutney. Divide the potato slices among the four pieces of bread, placing on top of the chutney layer. Take 1 to 2 tablespoons of chaat masala and sprinkle the four slices with potatoes to taste.
Distribute cucumber slices evenly across each piece of bread with a potato layer and sprinkle lightly with chaat masala. Repeat with beet slices, if using, and chaat masala. (Now you have: chutney, potato, chaat masala, cucumber, chaat masala, beet, chaat masala.)
Place another slice of bread, butter side up, on the potato-cucumber-beet layer. Top each slice with two pieces of cheese. Sprinkle with chaat masala, before distributing tomato slices to each sandwich. Layer the tomatoes on top of cheese and sprinkle with remaining masala.
Take last four remaining slices of buttered bread and spread the other side with butter, too. Then put a layer of chutney one side and place the bread chutney side down on the sandwiches. Place sandwich in sandwich press (both outside pieces of bread should be buttered at this point). Then grill until the bread is golden and the cheese somewhat melty.
Remove from grill and cut in half, ideally diagonally, and serve with remaining chutney on the side for dipping, as well as ketchup.