Start by heating your oil in a large skillet over medium-high heat until it shimmers. Season your chicken breasts generously with salt and pepper on both sides to ensure good flavor. Place the chicken in the hot pan and sear for about 3-5 minutes per side until golden brown, then remove to a plate.
In the same pan, toss in your halved potatoes, cherry tomatoes, garlic, and all your dry seasonings. Stir these ingredients frequently and let them cook for just a minute or two to wake up the spices. Once fragrant, stir in the chopped fresh spinach until it begins to wilt slightly into the mix.
While the veggies are sizzling, quickly whisk the cornstarch into the chicken broth in a small bowl. Pour this mixture into the skillet along with the heavy cream, stirring gently to combine everything. This liquid base will deglaze the pan and become that rich, creamy sauce we want.
Nestle the browned chicken back into the pan, surrounding it with the vegetables and sauce. Cover the skillet with a lid and reduce the heat to medium-low to maintain a gentle simmer. Let it cook for 15-20 minutes until the potatoes are fork-tender and the chicken is fully cooked through.
Once the cooking time is up, remove the lid and give everything a gentle stir. Sprinkle the freshly grated Parmesan cheese over the top and let it melt into the sauc. If you like, garnish with fresh herbs before bringing the skillet directly to the table for serving.