Melt 2 tablespoons of the butter in a large, nonstick skillet over medium-high heat. Add the chicken to the skillet and cook until browned, about 2 minutes per side. Remove the chicken to a clean plate.
To the same pan over medium heat, melt the remaining tablespoon of butter. Add the flour and whisk, cooking for about one minute.
Add the prepared shallots and garlic. Whisk and cook until fragrant, about one minute more.
Add the wine and bring to a low boil. Add the Dijon mustard and whisk until smooth.
Add the chicken broth and heavy cream and cook until simmering.
Whisk in the Dijon mustard to the sauce until smooth.
Stir in the fresh tarragon. Return the chicken to the sauce. And top each chicken breast with a lemon slice.
Lower the heat if necessary to keep the sauce at a low simmer. Cover the pan with a lid. Cook for about 10 minutes, until each chicken breast registers 165 degrees F in the thickest part.