Start by preheating your oven to 400F. Remove the ribs and seeds from the poblanos. Dice the poblanos and onion, and toss with the olive oil, ½ ts salt and ½ ts pepper. Once ready, add to a rimmed baking tray and roast for around 30 minutes. Check it at around 15 minutes in and toss if necessary to prevent burning and encouraging even cooking.
While your peppers and onion are roasting, butter both sides of your hamburger buns and lightly toast each side in a skillet set to around medium.
Next, season your ground beef with a mixture of ½ ts salt, ½ pepper, and ½ ts garlic powder. Shape the ground beef into 3 equal portions and try to flatten them down and make them a bit on the thin side. It's very important to LIGHTLY MIX as heavy handed mixing doesn't work well for burgers!
Now simply pan fry each side in a bit of butter on medium high. For a burger closer to medium well, fry the first side for around 4 minutes, flip, then fry the flip side for around 3 minutes. Please feel to adjust your cooking time to suit your tastes.
Adding the CHEESE! Layer a couple of pieces of American cheese on the top of the burgers during the last 45 sec to 1 minute of frying time on the 2nd side until the cheese is nice and melty!
Time to assemble your burger! Simply place the cheese laden burger on the bottom bun, top with as much of the roasted green poblano/onion mixture as you like (approximately ⅓ can be used for each of the 3 servings) and top with the top bun!