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Cut each block of halloumi in half horizontally through the middle to create 4 flat halloumi steaks in total.
For the umami butter, put all the ingredients into a bowl and mix until evenly combined, seasoning with a good pinch each of salt and pepper.
Brush the portobello mushrooms on one side with the umami butter and place them buttered side down on a medium-hot barbecue. Brush the other side thickly with butter while they are cooking. Turn the mushrooms over after 2–3 minutes and add the halloumi to the barbecue. Brush the surface of the halloumi with umami butter too. Keep brushing the mushrooms with the butter as they cook; do the same with the halloumi.
Towards the end of the cooking, toast the burger buns on the barbecue. Brush any remaining umami butter onto the toasted buns.
To assemble the burgers, place a mushroom, flat side up, on the base of each burger bun. Top with a halloumi steak and add a spoonful of sweet chilli or hot chilli sauce. Pile a big handful of rocket leaves on top. Spread some mayo on the bun lids and sandwich the burgers together. Tuck in straight away.