Boil the potatoes in salted water over medium-high heat until tender, about 15 minutes. Drain and keep warm.
If the chicken breasts are thick, slice them in half horizontally. Season with the Italian seasoning, salt and pepper.
Heat the oil in a large skillet over medium-high heat and sear the chicken for about 5 minutes per side until golden. It will finish in the sauce. Set aside.
Lower the heat to medium. Add the garlic and halved tomatoes and cook for 2 minutes until the tomatoes soften.
Whisk in the milk, cream cheese and parmesan and simmer gently, whisking, until smooth and slightly thickened, about 2 minutes. Keep it at a gentle simmer so the milk does not split.
Stir in the spinach, return the chicken and simmer for 4 minutes, spooning the sauce over, until the chicken reaches 74°C (165°F) inside.
Serve with the potatoes, spooning over plenty of sauce.