Heat the olive oil in a large skillet over medium-high heat.
Season the chicken breasts with salt and pepper, then add them to the skillet.
Cook the chicken for about 6-7 minutes on each side until golden brown and cooked through.
Remove the chicken from the skillet and let it rest on a cutting board.
In the same skillet, add the diced onion and sauté until translucent, about 3-4 minutes.
Add the minced garlic and sliced mushrooms, cooking for an additional 5 minutes until mushrooms are tender.
Stir in dried thyme to the mixture and cook for 1 minute to release its aroma.
Pour in the chicken broth, scraping the bottom of the skillet to deglaze and incorporate the fond.
Reduce the heat to low; add sour cream and Dijon mustard, stirring until combined.
Slice the rested chicken and place it back in the skillet, simmering for 5 more minutes in the sauce.
Taste and adjust seasoning with salt and pepper as needed.
Serve the creamy chicken stroganoff over egg noodles or rice, garnished with fresh parsley.