1Heat the broiler to high and arrange a rack in the middle. Place peppers on a baking sheet, cut side down, and broil until blackened and charred, about 15 minutes, rotating the pan as necessary.
2Transfer peppers to a medium bowl, cover tightly with plastic wrap, and let sit until cool enough to handle, about 15 to 20 minutes. Remove peppers from the bowl, discard any liquid, and wipe out the bowl. Peel the peppers (discarding the skin), coarsely chop, and return to the bowl.
3Add remaining ingredients and mix until the sweet and hot peppers coat the cheese.
4In a food processor fitted with a blade attachment, purée the mixture for about 2 minutes, until very smooth and creamy. (The mixture will be quite loose.) Refrigerate for about 30 minutes before serving to allow the dip to set.
5Place the mixture in a serving bowl and sprinkle it with a pinch each of Aleppo chile, Urfa chile, and paprika.