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1. Melt the butter and oil in a large skillet over medium heat.
2. Add the chicken breasts and brown on both sides.
3. Turn the heat to low and cook for 15 minutes, covered, or until the chicken is done.
4. Remove the chicken from the skillet and place on a serving platter.
5. Cover the platter with aluminum foil and keep warm.
6. Add the heavy cream to the skillet and scrape up the bottom bits.
7. Add the tarragon and mustard and cook for 5 minutes over medium heat, stirring constantly until thickened.
8. Season with salt and pepper, to taste.
9. Serve the chicken breasts with the sauce poured over the top.
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