Preheat the oven to 400°F (200°C).
Heat olive oil in a large skillet over medium heat, then add minced garlic and sauté until fragrant, about 1 minute.
Add diced chicken breasts to the skillet and cook until lightly browned, about 5-7 minutes.
Remove chicken from the skillet and set aside.
In the same skillet, combine chicken broth, heavy cream, cheddar cheese, and Parmesan cheese; stir until cheese melts and mixture is smooth.
Season the sauce with dried thyme, dried rosemary, salt, and pepper, then bring to a simmer without boiling over.
Add cubed potatoes to the sauce and stir until well coated, then return chicken to the skillet and mix gently.
Transfer the mixture to a baking dish and distribute evenly.
Bake in the preheated oven for 25-30 minutes, or until chicken is fully cooked and potatoes are tender.
Remove from oven and let cool for a few minutes before serving.
Garnish with chopped fresh parsley for added flavor and color.