Melt butter in large stockpot over low heat. Add leeks and a dash of salt. Cook about 7 minutes, until leeks are tender. Stir occasionally, taking care not to let them brown.
Add potatoes, onions, garlic chicken stock and paprika.
Bring to boil, then reduce to medium and cook for about 20 minutes, until potatoes are fork-tender.
While potatoes are cooking, char poblano pepper over a low flame on your gas burner, or under your broiler in your oven. Turn the pepper regularly so all sides are charred evenly. Seal it in a plastic and allow to cool. (The pepper will steam, allowing the skin to come off more easily.)
Once the pepper has cooled, rub the skin off, slice it open and remove the seeds. Dice the pepper.
Using an immersion blender or a standing blender, puree soup until it’s smooth. Add milk and pepper (and more salt, if desired) and give it another couple pulses.
Ladle into bowls and garnish with the poblanos, as well as bacon, cheese and whatever else you want. This soup requires lots of garnishment.