Heat olive oil in a large Dutch oven or heavy pot over medium-high heat. Brown the chicken pieces for 5-7 minutes per side, working in batches if needed to avoid crowding. Transfer browned chicken to a plate and set aside.

Add diced onion to the same pot and sauté for 3 minutes until softened. Stir in minced garlic and tomato paste, cooking for another minute until fragrant and the paste darkens slightly.

Pour in chicken broth, scraping up any browned bits from the pot bottom with a wooden spoon. Return chicken to the pot and add sliced carrots, cubed potatoes, bay leaf, thyme, rosemary, salt, and pepper.

Bring the mixture to a simmer, cover partially, and cook for 20-25 minutes until vegetables soften and chicken cooks through. This creamy hearty chicken stew recipe develops better flavor when simmered gently rather than boiled aggressively.

Mix cornstarch with water in a small bowl to form a slurry. Stir this mixture into the pot slowly, stirring constantly until the sauce thickens enough to coat a spoon, about 2-3 minutes.

Reduce heat to low and stir in heavy cream and frozen peas. Simmer for 5 more minutes, then taste and adjust seasonings with additional salt and pepper as needed.

Remove the bay leaf and serve immediately while the dish remains piping hot and steaming beautifully.