Preheat oven to 400°.
Place potatoes in a large bowl and toss together with sesame seeds, sesame oil, 1/2 tsp salt, and 1/4 tsp pepper. Transfer to a sheet pan and set bowl aside. Spread potatoes into an even layer and bake for 20 minutes.
While baking, add pork to the empty bowl along with ginger, garlic, ½ tsp salt, and ¼ tsp pepper. Gently combine with your hands. Form into two patties that are slightly wider than your buns and make an ident in the center of each with your thumb. Set aside.
In a small bowl combine carrot, daikon, cilantro, rice wine vinegar, and gochugaru. Set aside.
Flip potatoes and return to oven for another 15-20 minutes, or until well browned.
While potatoes finish cooking, add canola oil to a large cast-iron skillet over medium heat. When oil shimmers add patties and cook for about 4-5 minutes per side, until browned and firm with internal temperature of 160°. Remove to a plate.
Add burger buns to the skillet cut-side-down and toast for 2-3 minutes. Spread mayo on buns and assemble burgers with bottom bun, red onion, burger patty, slaw, and top bun. Transfer potato wedges to a medium bowl, toss with hoisin to coat, and serve with burgers.