If using chicken breasts, cut them in half horizontally to form thinner steaks, ensuring they cook evenly. Sprinkle the chicken on both sides with the salt and black pepper to taste. This preparation helps the chicken cook quickly and stay juicy.
Heat 2 tablespoons of oil (reserved from the sun-dried tomato jar) in a large skillet over high heat. Add the seasoned chicken and cook until golden brown on both sides—about 6 minutes total for thigh or 4 minutes for breast. Once cooked, remove the chicken onto a plate and keep it warm. I like to loosely cover it with foil to retain the heat.
Lower the heat to medium-high and add the minced garlic to the same skillet. Sauté for about 15 seconds until fragrant and just turning golden. Pour in the dry white wine and bring it to a simmer, scraping up any brown bits from the bottom of the pan to enrich the sauce. Let the wine simmer for about 1 minute, or until the smell of alcohol fades, indicating it has evaporated.
Mix in the Dijon mustard, then pour in the chicken broth and heavy cream. Add the grated parmesan cheese and the drained, sliced sun-dried tomatoes. Bring the mixture to a gentle simmer, then reduce the heat to medium and cook for 2 to 3 minutes, stirring regularly to help dissolve the cheese and slightly thicken the sauce. Taste and adjust with additional salt or black pepper as needed. I always recommend tasting before adding extra seasoning, since parmesan and sun-dried tomatoes are already salty!
Stir the basil leaves through the finished sauce, then return the cooked chicken (from Step 2) and any juices that have collected on the plate to the skillet. Spoon some sauce over the chicken and simmer everything together for 1 more minute to let the flavors meld. I like to add the basil at the end so it stays bright and aromatic.
Serve the chicken and sauce immediately, ideally over mashed potatoes, creamy mashed cauliflower, pasta, or with bread to soak up the delicious sauce. Garnish with more fresh basil or parmesan if desired.