Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Pat the chicken pieces dry with paper towels, then season generously with salt and black pepper on both sides before adding to the hot oil.
Sear the chicken for 3-4 minutes per side until the exterior develops golden-brown color, working in batches if needed so pieces aren't crowded. Remove the seared chicken to a clean plate and set aside for later use in the recipe.
In the same pot, add diced onion and cook for 2-3 minutes until softened, then stir in minced garlic and tomato paste, cooking for another minute to release the aromatics. Add sliced carrots and cubed potatoes, stirring to combine all the vegetables with the oil and flavorings.
Return the seared chicken pieces to the pot along with chicken broth, diced tomatoes, dried thyme, rosemary, and bay leaf. Bring the tender crowd chicken stew recipe to a gentle boil, then reduce heat to medium-low and simmer uncovered for 35-40 minutes until the chicken is fall-apart tender.
In a small bowl, whisk cornstarch with 2 tablespoons cold water until no lumps remain, then slowly stir this mixture into the simmering stew. Cook for 2-3 minutes to thicken the broth slightly, then add green peas and cook for another 2 minutes until heated through.
Taste and adjust salt and pepper as needed before serving warm. Remove the bay leaf if you spot it, then ladle into bowls for immediate enjoyment.