A French bistro classic. Chicken "supremes" — breasts with the upper part of the wing attached — make for a beautiful presentation. If they're not available, use bone-in, skin-on chicken breasts. Using beurre manié (made from equal parts butter and flour) is a classic sauce-thickening trick.
2 tbsp olive oil
6 bone-in, skin-on chicken supremes
Salt and pepper, to taste
3 large shallots, sliced
1 small clove garlic, minced
1/2 cup dry white wine
1 cup chicken broth
1/2 cup 35% cream
1 tsp Dijon mustard
1 tbsp butter, at room temperature
1 tbsp all-purpose flour
1 tbsp finely chopped fresh tarragon
Step 1: Preheat oven to 400°F. Heat oil in a large, wide skillet over medium-high heat. Pat chicken dry with paper towel; season with salt and pepper. Add chicken to skillet skin-side-down and cook 3-5 minutes, or until deep golden. Flip and cook another 2 minutes. Transfer to large baking pan and bake 20-25 minutes, or until cooked through.
Step 2: Meanwhile, to make tarragon sauce, add shallots and garlic to skillet, reduce heat to medium and cook 4 minutes, or until shallots have softened. Add wine and bring to a boil. Reduce heat and simmer until reduced by half. Add chicken broth, bring to a boil and cook 3 minutes. Strain, reserving liquids and discarding solids. Return liquids to skillet or a small pot, bring to boil and whisk in cream and Dijon.
Step 3: Mash butter and flour together in a small bowl. Add 1/4 cup of hot chicken broth mixture to beurre manié and stir until combined (it will be very thick). Add entire mixture back to hot chicken broth and stir until combined.
Step 4: Add chopped tarragon and season with more salt and pepper. Spoon sauce over chicken to serve. Serve with rice and additional mustard if desired.