Start by halving the cherry tomatoes and mincing the garlic cloves. Chop the fresh basil finely and set it aside. Season the chicken breasts generously on both sides with salt, pepper, and dried oregano.
Heat the olive oil in your skillet over medium-high heat. Once hot, add the chicken breasts. Sear each side for about 4-5 minutes until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Toss in the halved cherry tomatoes and cook until they start to soften and release their juices, about 3-4 minutes.
Pour in the heavy cream and stir well, scraping any browned bits off the bottom of the pan. Let the sauce simmer for 2-3 minutes to thicken slightly. Stir in the chopped fresh basil, reserving a little for garnish.
Return the chicken breasts to the skillet, spooning some sauce over the top. Allow everything to simmer together for another 2 minutes so the flavors meld.
Sprinkle grated Parmesan cheese generously over the chicken and sauce. Garnish with the reserved basil. Serve hot and enjoy the creamy, flavorful goodness.