Cook chorizo in a medium frying pan over medium heat, stirring occasionally, until browned, about 5 minutes. Let cool.
Preheat oven to 400°. In a small bowl, stir together cream cheese, cheddar, chorizo, cilantro, and chile flakes.
Lightly sprinkle a work surface with flour. Unroll crescent roll dough and lightly roll to about 9 by 13 in. to eliminate seams. Using a sharp knife or pizza cutter, cut dough crosswise into 24 strips, each about 1/2 wide.
Fill each pepper half with cream cheese mixture, mounding it slightly. Wrap each pepper half all the way around with a strip of dough, leaving space between successive wraps and tucking ends in. Place peppers on a parchment paper-lined baking sheet and brush tops of dough with beaten egg.
Bake until pastry is golden brown, 10 to 12 minutes. Transfer to a platter and let cool about 10 minutes. Using a pastry bag or a resealable plastic bag with the corner cut off, pipe 2 dots of sour cream onto each pepper for eyes. Place an olive piece on each sour cream dot and serve immediately.