Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Working in batches to avoid crowding, sear chicken pieces until golden brown on both sides, approximately 3-4 minutes per side. Transfer cooked chicken to a plate and set aside.
In the same pot, sauté diced onion and minced garlic for 2-3 minutes until fragrant and softened. This aromatic base creates the foundation for your one pot chicken dinner's rich flavor profile. Stir constantly to prevent burning.
Add sliced carrots and cubed potatoes to the pot, cooking for 3-4 minutes while stirring occasionally. Pour in chicken broth and diced tomatoes, scraping up any browned bits stuck to the bottom—these contain incredible flavor.
Return the seared chicken to the pot along with dried thyme, rosemary, and bay leaves. Bring to a boil, then reduce heat and simmer for 25-30 minutes until chicken is cooked through and potatoes are tender when pierced with a fork.
Stir in fresh spinach and heavy cream during the final 2 minutes of cooking. The spinach wilts quickly while the cream creates a luxurious sauce that coats every ingredient. Season with salt and pepper to taste before serving.