Broil poblano pepper until skin is blistered on all sides (this took 20 minutes in my toaster oven, but might take less time in a regular oven); alternatively grill the poblano pepper. Place blistered poblano pepper in a bowl and cover with plastic wrap; let sit 20 minutes. Remove skin, stem and seeds.
Place peeled, seeded poblano pepper in food processor and process until chopped fine. Add garlic, parsley, chives, dill, mayonnaise, sour cream, salt and pepper. Process until smooth, leaving a few flecks of green if you like.
Adapted from The Pioneer Woman