Prepare the chicken by tenderizing with a meat hammer, if desired. Then sprinkle both sides with salt and pepper.
Melt butter and olive oil in a skillet over medium heat.
Cook the onion until tender.
Add minced garlic and cook for a minute more.
Put the chicken breasts into the skillet, and cook on both sides for several minutes, searing if desired.
Add the water and sprigs of thyme, and cover and let simmer for 15 minutes.
When chicken is cooked through, add several squirts of Dijon mustard over the chicken.
Add the tablespoon of lemon juice, and stir everything around until a sauce is formed.
If you need to, reduce the liquid for a few more minutes.
When it is finished cooking, take the skillet off the heat, add in a swirl of heavy whipping cream. At least a tablespoon or more if desired.
Stir everything well, and serve!