Flatten the chicken breasts (or you can also buy them flattened) to ensure an even cooking time. You’ll do that by placing them between sheets of plastic wrap, and gently pressing on top with a plate or flat baking sheet. Dry them with a paper towel before you begin.
Mix the 1/4 cup olive oil, Meyer lemon juice, 2 crushed garlic cloves, 1/2 teaspoon salt and 1/2 teaspoon black pepper in a small bowl.
Pour the marinade over the chicken breasts on a plate, cover and refrigerate for about an hour.
When they're ready, remove from the marinade, and discard the rest.
Preheat oven to 425°F.
Place the chicken breasts in a large baking dish.
In a skillet, melt the butter, and add the remaining 2 cloves minced garlic, along with the oregano, rosemary, and Meyer lemon zest. Cook for about 2 minutes, until fragrant.
Stir in the cherry tomatoes, and continue to cook for another 2 or 3 minutes.
Add the heavy cream and grated Parmesan, and stir until well blended.
Pour over the chicken breasts, and bake in the oven for 15 to 20 minutes, until bubbling, and the chicken is cooked all the way through.
Add the spinach, stirring lightly to blend into the sauce, and return to the oven for another minute or two, until the spinach is wilted.