Using tongs, grill the poblano on the stovetop until the skin is blackened. Place in a paper or plastic bag and set aside to cool for about 20 minutes.
Remove the skin and seeds from the poblano under running water, then dice.
Add the dark and light meat ground turkey to a bowl. Add the poblano, jalapeno, salt and pepper. Drizzle in the olive oil and mix together. Form the mixture into 10 to 12 patties.
Heat a grill or grill pan to medium high and cook the burgers until charred and golden on the outside and cooked all the way through, 5 minutes per side. Toast the buns cut-side down on the grill until golden, a couple of minutes.
Serve the burgers in the buns (or wrap in lettuce leaves) with sliced tomato, red onion, lettuce, mustard, mayonnaise and ketchup.