In a pot, saute the garlic and onion in some oil.
When onions are softened, add in the Chorizo de Bilbao.
Add the marinated chicken and lay it out evenly at the bottom of the pan to cook evenly. Scoop the sauteed garlic, onion, and Chorizo de Bilbao on top of the chicken so that they do not overcook or burn. The goal here is to LIGHTLY BROWN the chicken, not fry it. Lower the heat slightly and cover. You will notice that the chicken will not appear fried but will produce a "soup" instead if you do this. Make sure to turn the chicken as you don't want only one side to brown.
If you have more chicken pieces than space, do them in batches. When the first batch is lightly browned on both sides, put in the remaining chicken and place the first batch on top of them. Don't forget to cover. This step should take around 5 to 10 minutes.
Add the sliced chicken franks and chicken stock. Lower the heat and let it simmer covered for 20 minutes.
Add the potato, carrot, and cream. Mix, then simmer covered for another 8 minutes.
Add the bell peppers and mushroom, mix, and cook for another 3 minutes.
Turn off the heat and just let it sit for a few minutes before serving.