Thinly slice half the onion and set aside. Finely chopped the remaining onion half and place in large bowl with mince, mushrooms and herbs. Season with pepper. Mix with clean hands until well combined. Divide into 2 even portions. Shape portions into 1cm-thick patties.
Heat oil in a medium, deep non-stick frying pan over medium heat. Add sliced onion. Cook, stirring, until light golden. Transfer to a plate. Cover with foil to keep warm.
Add patties to same pan. Cook for 4-5 minutes on each side over medium-high heat, until evenly browned and cooked through.
Split rolls in half and toast lightly. Spread avocado over cut-sides of rolls. Top bases with lettuce, patties, tomato, beetroot, onion and chutney. Cover with roll tops to serve.

Packaged fresh cooked beetroot is available from the fruit and vegetable section in major supermarkets.
Hamburger patties can be made one day ahead. Keep covered in fridge, or up to 2 months in freezer. Thaw overnight in the fridge before cooking.
Check labels on chutney and choose the brand lowest in sodium.