In a large deep heavy skillet stir together beer, mustard, and ketchup.
Cut 1 onion into thick slices and add to beer mixture.
Bring beer mixture to a boil and in it simmer bratwursts, uncovered, turning occasionally, 20 minutes.
Remove bratwursts from beer mixture, discarding beer mixture. Cut remaining 3 onions into thick slices, keeping slices intact.
Grill bratwursts with onion slices on an oiled rack set 5 to 6 inches over glowing coals, turning onions once, until bratwursts are cooked through and golden brown and onions are cooked through, about 5 minutes.
Put a pair of “brats,” cut in half lengthwise and stacked, on each roll.
Top brats with grilled onion, pickles, and mustard.