Season the chicken with salt and pepper. To a very hot pan add 2 tablespoons of olive oil. Add chicken until the pan is covered but no pieces are overlapping. Cook until just the outsides of the chicken have a light browning. Continue until you have browned all the chicken pieces. Add more olive oil if the pan becomes dry. The chicken does not need to cook all the way through, as it will finish cooking in the stew. Set browned chicken pieces into a large stew pot.
Sauté onions in oil until they are lightly browned. Deglaze the pan with red wine. Scrape the bottom of the pan to release any cooked bits and then transfer into the stew pot
Sauté mushrooms in oil until they are golden brown. When the mushrooms are nearly done add in garlic. Cook for 1 minute, deglaze the pan with red wine, then transfer into the stew pot.
To the empty sauté pan add Brandy and cook for 30 seconds then add to the stew pot.
Add raw carrots, canned tomatoes, and chicken stock into the stew pot. Cook over low heat for 30 minutes.
Add butter and flour into a small pan over low heat. Stir to combine, until no clumps remain in the flour. This mixture is known as a roux and is used to thicken the stew. Add have of the roux into the stew. Stir and wait 5 minutes. If you would like a thicker stew add the second half of the roux.
Into the stew pot add the frozen peas and pearl onions. Cook for 10 additional minutes and serve!
Keyword chicken, chicken coq au vin, classic, stew