Roast the poblano pepper. Start by charring or broiling your poblano pepper until blackened. I use a pair of tongs to rotate it over the flame on my gas burners. Alternately, place it on a baking sheet and broil on high heat, turning the pepper once, until blistered all over. Place the charred pepper in a ziplock bag or a heat safe bowl and cover with plastic wrap. Once the pepper is cool, peel and dice it.
Mix the burgers. Combine the ground turkey and remaining ingredients together (except for the sliced cheese) in a bowl with salt and pepper. Mix gently by hand until just combined and all the ingredients are evenly mixed.
Shape the patties. Divide the mixture into 4 and shape into patties with a depression in the middle. Place the shaped burgers on a plate or small baking sheet lined with parchment paper. Transfer the burgers to the freezer for 15-20 minutes, until firmed up.
Mix the chipotle mayo. Combine all the ingredients in a small bowl and mix well. Season with salt and pepper and transfer to the fridge until ready to use.
Cook the burgers. Heat a grill pan or cast iron skillet over medium heat. Let the pan preheat for about 5 minutes. Add a bit of neutral oil. Once the oil is hot, cook the burgers for about 5 minutes per side, until browned. Add the pepper-jack cheese after flipping the burgers so that it has time to melt. Use a meat thermometer to ensure the burgers are cooked to 165 F.
Assemble the burgers. Toast the buns and spread one side with chipotle mayo and the other side with guacamole. Place the burgers on the bun and top as desired.