Preheat air-fryer to 200°C.
Slice kūmara (skins on) into 2cm rounds to create "buns". Drizzle with oil and place in air-fryer for 15-20 minutes, or until cooked through and golden.
Roll mince into small patties, around the same size as your kūmara rounds. Heat oil in a pan on a medium-high heat. Cook patties for 3-4 minutes each side, or until cooked through. Slice cheese and set aside.
Assemble burgers using the kūmara pieces as your bun, filled with beef patties, cheese, gherkins and topped with burger sauce.