Preheat an oven to 425°F. Line a sheet pan with foil. Once the oven is hot, toss the cherry tomatoes with the tbsp of olive oil to coat evenly. Sprinkle with salt and pepper to taste. Roast for 30 minutes while you prepare the chicken, tossing once during the roasting process.
In a large skillet, heat the vegetable oil over medium-high heat. While the pan is heating, sprinkle the chicken breasts with kosher salt, freshly ground black pepper, and garlic powder, to taste.
Once the skillet is hot, add the chicken breasts and sear for 4 minutes on one side before turning and searing on the opposite side for 4 more minutes. Remove from the pan to a plate and allow to rest.
In a large, separate pot, bring a gallon of water to a rapid boil.
While the water is waiting to boil, add the shallots and minced garlic to the skillet that you seared the chicken in. Sauté for 3 minutes or until fragrant and translucent. Deglaze the pan with the white wine, making sure to scrape up the browned bits from the bottom of a pan with a wooden spoon. Allow the liquid to reduce by three-quarters.
Stir in the chicken stock, bring to a boil, and allow to reduce by 1/2. While your stock is reducing, cut the chicken breast into 1" chunks. Your water should also be boiling, add the pasta and cook according to the package directions.
By now your tomatoes should be roasted and caramelized. Remove them from the pan with a spatula (it's okay if they look really dark), and set them aside.
Remove the sauté pan from the heat and slowly stir in the heavy cream. Return the pan to the burner and reheat on low. Add the chicken breast, the tomatoes and the spinach. Stir to combine.
Drain your pasta and add to the pan. Adjust the seasoning to your preference. Sprinkle in the parmesan cheese and serve.