Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Cut potatoes into 1/2-inch-thick wedges. Toss on a baking sheet with a large drizzle of oil and season with salt and pepper. Roast on top rack until golden brown and crispy, 20-25 minutes.

Meanwhile, trim, peel, and grate carrot on the largest holes of a box grater; transfer to a medium bowl. Trim and halve cucumber lengthwise; thinly slice into half-moons. Halve lime. Add cucumber, juice from whole lime (both limes for 4 servings), and half the sesame oil (you’ll use the rest later) to bowl with grated carrot; toss to combine. Season with salt and pepper.

In a small bowl, combine mayonnaise and sriracha to taste. Season with salt and pepper.

In a large bowl, combine pork and remaining sesame oil. Season generously with salt (we used 3/4 tsp; use 11/2 tsp for 4 servings) and pepper. Form into two equal-sized patties (four patties for 4), each a bit wider than a burger bun.

Heat a drizzle of oil in a large pan over medium-high heat. Add patties and cook until browned and cooked through, 4-6 minutes per side. Turn off heat; carefully pour out any excess grease from pan. Stir in hoisin sauce; flip patties to fully coat.

While patties cook, halve and toast buns. Fill toasted buns with patties, any remaining hoisin from pan, and a bit of slaw and sriracha mayo. Serve with potato wedges and any remaining slaw on the side. TIP: If you’ve got some, serve with ketchup for dipping.