Tenderize chicken breasts by pounding them to half thickness with a meat tenderizer. Season chicken breast on both sides with salt, pepper, and dried oregano. Heat oil in a large frying pan over medium heat.
When the oil is hot, add the seasoned chicken to the pan and cook on medium for 5 minutes each side. Remove the chicken from the pan, reduce the heat to medium-low and add the minced garlic. Simmer for 2-3 minutes.
Add the cherry tomatoes to the pan whole and season with a sprinkle of salt and pepper. Cook on medium low until the cherry tomatoes blister and begin to burst, about 6 minutes
While the tomatoes cook, whisk together heavy cream, tomato paste and chicken broth. Smash down any of the blistered tomatoes that haven't burst yet and pour the liquid mixture into the pan
Stir to combine and allow the mixture to start to simmer. Slowly pour in the parmesan cheese and stir until it is completely melted and mixed into the sauce. Please the chicken back in the pan and toss to coat with the sauce. Simmer for 3 more minutes and serve with ribbons of fresh basil.
Optional: If you would like to serve this with pasta, boil 8oz of pasta. Reserve 1/4 cup of the pasta water. Add the cooked and drained pasta, along with 1/4 cup pasta water into the pan with the chicken and the sauce.