Start by seasoning your chicken with salt and pepper and then dredge it in all-purpose flour until it’s evenly coated. In a large, deep pan over medium-high heat, add a couple tablespoons of cooking oil like avocado or olive oil and heat until the oil is hot.
Carefully place the chicken fillets into the pan, being careful not to overcrowd the pan (do this in multiple batches if the chicken doesn’t fit with a decent amount of space between fillets) and fry the fillets until they are golden brown on each side. When finished, remove chicken from the hot oil and set aside.
Turn down the heat to medium-low and add the butter, allowing it to melt fully into the oil. Add in the diced onions and minced garlic and sauté for just a few minutes until the onions start to become translucent.
Deglaze the pan with the chicken stock, making sure to carefully scrape up the chicken flavor as the hot chicken stock loosens it from the bottom of the pan. Season the sauce with thyme and red pepper flakes, then mix in the heavy cream and grated parmesan until the parmesan is fully melted.
Add the sundried tomatoes and place the chicken pieces back into the sauce. Taste the sauce and season with salt if necessary. Let the sauce simmer for 3-5 minutes to thicken. A dish with heavy cream sauce is usually best eaten hot and right away over a starch like pasta or rice.