You can make sliders or regular size burgers, I try to plan one chile for each burger. First roast your peppers on the grill or in the oven. I use my broiler on low setting when I roast them in the oven. Once cool remove the skin and seeds and dice. Crumble or grate Cotija cheese. This is a Mexican crumbling cheese that is very similar in flavor and texture to Feta.
In a bowl mix together diced chiles and crumbled cheese to whatever ratio you like. Then add ground chuck and your favorite burger seasonings in bowl and mix together. Form balls and roll around in hand until they become cohesive, then flatten into patties.
Grill or cook in skillet or on griddle, add cheese on top when done.
NOTE: If you like this idea but not really interested in roasting peppers, you can buy 4 oz cans of diced green chiles, be sure to put them in a strainer and remove as much juice as possible, then mix with cheese and add to meat.