Season the chicken breast fillets with salt and pepper. Fry over medium-high heat for 3-4 minutes per side until golden. Transfer to a baking dish. Slice the tomato and arrange overlapping on the chicken like roof tiles. Season lightly with salt and pepper. Slice the mozzarella and place on top of the tomatoes.
Mince the garlic. Strip the oregano leaves from their stems and chop finely. In a bowl, combine the cream with salt, pepper, minced garlic, and chopped oregano. Pour the sauce over the chicken and tomato. Bake in a 180-200°C (356-392°F) oven for roughly 30 minutes until the thickest part of the chicken reaches 74°C (165°F) internally.