Toss together chicken, tomato sauce and minced chipotle peppers; stir in cheese.
Whisk together beaten egg with 1 tbsp. water. Lightly brush edges of discos with some of the egg wash. Spoon 2 tsp. chicken filling into center of each disco. Fold over and pinch edges together to seal.
Meanwhile, pour enough oil into large saucepan to come 3 inches up side; heat over medium heat until instant-read thermometer reads 350°F. Working in 4 batches, carefully drop mini empanadas into hot oil; fry for 2 to 3 minutes or until golden brown all over. Using slotted spoon, transfer empanadas to paper towel–lined tray. Sprinkle with cilantro. Serve with sour cream.
For extra spice, add an additional 1 tbsp. of chipotle pepper in adobo sauce. Serve with guacamole.