2) Brush the chillies with oil and season with salt and pepper. Grill for about 12 minutes, turning often, until blistered on all sides and soft.
3) Remove the chillies from the grill, place in a bowl, cover with cling film and leave for 15 minutes.
4) Peel, stem and seed the chiles. Slice and set aside.
5) Make 4 loosely-packed burger patties by tossing some of the meat from hand to hand. press your thumb into the center of each patty to make a little well. (At this point, you can chill or even freeze the burgers briefly so that they hold their shapes better when cooked.)
6) Brush with oil and season with salt and pepper.
7) Grill for about 8 minutes, until slightly charred on both sides and cooked to medium doneness.
8) Top each burger with 2 slices of cheese, close the cover of the grill and continue cooking for about 30 seconds or until the cheese just melts.
9) Put the buns on the grill, cut side down and grill for about 15 seconds until slightly charred.
10) Place the burgers on the bottom half, put a few slices of the poblano on top of the cheese and cover with the burger tops.