Season chicken with 1 teaspoon salt and 1/2 teaspoon pepper.
Heat olive oil in a Dutch oven over medium heat. Working in batches, add chicken to the Dutch oven in a single layer and cook until golden brown and cooked through, reaching an internal temperature of 165 degrees F, about 4-5 minutes per side; set aside.
Stir in tomato paste, garlic, oregano, thyme and red pepper flakes until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the Dutch oven.
Stir in chicken stock, heavy cream and sun-dried tomatoes; season with salt and pepper, to taste.
Bring to a boil; reduce heat and simmer, stirring occasionally, until slightly thickened and flavors have blended, about 5 minutes. If the mixture is too thick, add more stock as needed.
Stir in Parmesan and basil. Return chicken to the Dutch oven.
Serve warm.
Notes
Tomato paste adds so much flavor. Tomato paste is a key ingredient in Marry Me Chicken, adding body and richness in small amounts without adding too much liquid to the dish. Opt for tomato paste in a tube, using up only what you need at a time without having to open up a whole can.
Choose a wine you will drink. A dry white wine (pinot grigio or sauvignon blanc) is great here – it does not have to be anything fancy or overpriced. Just something you don’t mind sipping on since you will have an open bottle.
Deglaze with wine. This is key to scraping up all the browned, caramelized bits stuck to the bottom of the pan (called fond) after searing the chicken. This is where all the flavor is!
Use heavy cream. Half-and-half (or whole milk) can be used, if needed, but heavy cream will yield the ultimate level of creaminess, whereas lower-fat dairy products (half-and-half or milk) will be a little more watery and prone to curdling.
Use dry-packed sun-dried tomatoes. These will be soft and brightly colored without being overly greasy (also great for snacking!).
Freshly grated Parmesan goes a long way. Pre-shredded cheese contains anti-caking agents that can make the sauce gritty. Grate fresh Parmesan (using a microplane) for a smooth, velvety consistency.
Let it simmer and reduce. Let the sauce simmer gently until it coats the back of a spoon.