Preheat the oven to 200C, fan-forced. Line an oven tray with baking paper. Quarter the unpeeled potatoes. Put the potato wedges on the lined tray, drizzle with 2 tsp olive oil, scatter with 1 tsp barbecue seasoning, season lightly with salt and pepper and toss to coat. Roast for 25 mins or until golden and tender.
Step 2 — Make patties
Meanwhile, put the beef mince, breadcrumbs, remaining barbecue seasoning and 1 egg in a large bowl. Using damp hands, combine well, then shape into 2 equal patties, slightly larger than the base of a bun.
Step 3 — Cook patties
Heat 1 tsp olive oil in a medium frypan over medium-high heat. Cook the patties for 3 mins each side or until cooked through.
Step 4 — Toast buns
While the patties are cooking, halve the buns through the middle. Put on an oven tray, cut-side up, and bake for 4-5 mins until lightly toasted.
Step 5 — Dress spinach
While the buns are toasting, put 1 tsp extra virgin olive oil and ½ tsp white wine vinegar in a large bowl, season with salt and pepper and whisk to combine. Add the spinach and toss to coat.
Step 6 — Get ready to serve
Thinly slice the tomato. Spread the buns with half the aioli. Divide the patties, tomato and half the spinach among the bun bases, then sandwich with the bun tops. Serve with the potato wedges, remaining aioli and remaining spinach.