Peel and finely chop carrots and potatoes. Transfer to a pot, cover with water and cook until firm but not mushy, it will take approx 5 minutes after the water starts to boil.
Seed the guajillo peppers and place them in a bowl, add the garlic clove and cover with boiling water. Place a kitchen towel on top and let them rehydrate for 20 minutes.
Cover baking sheets with parchment paper, or grease them in case you don’t have the parchment paper. Set aside.
Shred the cheese and chicken, put them back in the fridge.
Place guajillo peppers, ⅓ cup of the liquid from which the guajillos were rehydrated, garlic clove, oregano and salt in a blender or food processor and mix until smooth. Strain the sauce.
Heat a tablespoon of oil in a big skillet, pour in sauce and fry for a minute. Add chicken and vegetables. Mix well. Turn off heat and set aside.