Preheat the oven to 220C, fan-forced. Line 2 oven trays with baking paper. Peel the potatoes and thinly slice. Stack the slices, then cut into matchsticks and put on a lined tray. Drizzle with 2 tsp vegetable oil, scatter over the sesame seeds, season with salt and pepper and toss to coat. Bake on the upper oven shelf, turning halfway, for 25-30 mins until golden.
Step 2 — Make cucumber kimchi
While the fries are baking, peel the cucumber into ribbons with a vegetable peeler. Combine 1 tsp chilli paste (see Make it yours), 1 tsp white vinegar and 1 tsp sugar in a large bowl. Add the cucumber and toss to combine.
Step 3 — Cook patties
Combine the remaining chilli paste, 3 tsp sugar and 1 tbs water in a bowl and season with salt and pepper. Heat 1 tsp vegetable oil in a medium frypan over medium-high heat. Add the beef patties to the pan, season with salt and pepper, then cover and cook for 4 mins each side. Add the chilli mixture and cook, turning the patties, for 1-2 mins until glazed.
Step 4 — Toast buns
Meanwhile, cut the rolls in half. Put on the remaining lined tray, cut-side up, and bake on the lower shelf for 5-6 mins until lightly toasted. Thinly slice the spring onions on an angle. Combine the spring onion and 2 tbs mayonnaise in a bowl.
Step 5 — Serve up
Spread the roll tops with the spring onion mayo. Layer the bases with the patties and cucumber kimchi, then sandwich with the tops. Serve with the fries and enjoy!
Step 6 — Make it yours
We've suggested this amount of Korean chilli paste (known as gochujang) in the cucumber kimchi and glaze for flavour, but feel free to reduce to taste if you prefer less heat.