Heat olive oil in a large Dutch oven over medium-high heat. Season chicken pieces with salt and pepper, then brown them 5-7 minutes per side until golden. Remove chicken and set aside on a clean plate.
In the same pot, sauté diced onion 3-4 minutes until softened and fragrant. Add minced garlic and cook 1 minute more, stirring constantly to prevent burning.
Return the browned chicken to the pot along with carrots, potatoes, thyme, rosemary, and bay leaves. Pour in chicken broth and diced tomatoes, stirring gently to combine all ingredients evenly.
Bring the mixture to a boil, then reduce heat to low and simmer covered for 25-30 minutes. The one pot chicken stew recipe is ready when potatoes are fork-tender and chicken reaches 165°F internally.
Stir in fresh spinach and cook uncovered 2-3 minutes until wilted and vibrant green. In a small bowl, whisk cornstarch with water to create a slurry, then drizzle into the stew while stirring. Simmer 2 more minutes until thickened to your preferred consistency.
Taste and adjust seasonings with additional salt, pepper, or herbs as needed. Remove bay leaves before serving to avoid accidentally biting into them.