Season chicken cutlets with salt and pepper on both sides.
In a skillet over medium-high heat, heat olive oil. Working in batches, cook the chicken cutlets on both sides until cooked through. The chicken is done when the internal temperature reaches 165°F/74°C using a kitchen thermometer. This takes about 4-5 minutes per side. Remove the chicken onto a plate, set aside and keep warm.
Melt butter and add garlic to the center of the pan, sauté for 30 seconds, then deglaze the pan with chicken stock, wine, or water.
Add heavy cream, dijon mustard, lemon juice, and tarragon. Season with salt and pepper, and whisk or stir and let the sauce simmer for 4-5 minutes over gentle heat.
Return the chicken back to the skillet, spoon the sauce over the chicken and remove from heat. Garnish with chopped fresh parsley if desired, and serve over mashed potatoes, pasta, or rice.