Season both surfaces of the chicken breasts evenly with kosher salt, freshly ground black pepper, and oregano.

Warm the olive oil in a large pan over medium-high heat. Once the oil is hot, place the seasoned chicken breasts in the pan and cook for approximately 5 minutes per side, or until nicely browned and fully cooked. Transfer the chicken to a plate and set it aside.

Add the unsalted butter to the same pan and allow it to melt. Stir in the freshly minced garlic and sauté for approximately 30 seconds to 1 minute, just until aromatic. Keep the garlic moving so that it does not scorch.

Place the halved cherry tomatoes into the pan and cook until they soften and begin to burst.

Add the baby spinach and stir it through the tomatoes. Continue cooking for a couple of minutes, stopping once the leaves have just started to wilt.

Pour the cream into the pan, then stir in the grated Parmesan. Season the sauce lightly with additional salt and black pepper. Mix thoroughly, reduce the heat, and bring the sauce to a gentle simmer.

Return the cooked chicken breasts to the pan. Simmer them in the creamy tomato and spinach sauce for 5 to 7 minutes, occasionally spooning the sauce over the chicken so each piece remains thoroughly coated.

Finish the dish with a squeeze of fresh lemon juice and a scattering of chopped fresh parsley. Serve the chicken hot, topped generously with the creamy sauce, cherry tomatoes, and spinach.