01 -
Place each chicken breast half between two sheets of plastic wrap and pound with a meat mallet or rolling pin to ½-inch thickness. In a shallow bowl, combine 2 tablespoons flour, kosher salt, and black pepper. Lightly dredge each cutlet in the flour mixture, shaking off excess; set aside.
02 -
Heat a large heavy-bottom skillet over medium heat. Melt 2 tablespoons butter with canola oil. Add chicken cutlets and cook undisturbed until golden brown on the underside, about 4 minutes. Flip and cook another 3 to 4 minutes. Transfer cutlets to a plate and tent with foil. Repeat with remaining cutlets, adding butter or oil as needed.
03 -
Remove any browned residue from skillet with paper towel and return to medium-high heat. Pour in chicken broth or wine and bring to a boil, scraping up browned bits. Cook 2 minutes, then add heavy cream. In a small bowl, combine remaining 1 tablespoon flour and 1 tablespoon butter into a smooth paste and whisk into the sauce. Reduce heat and simmer until sauce thickens and coats the back of a spoon, 3 to 5 minutes. Stir in lemon zest and juice, fresh tarragon, and adjust seasoning to taste.
04 -
Return chicken cutlets to skillet and simmer in sauce for 2 minutes until warmed through. Serve with rice, pasta, or mashed potatoes, garnished with extra tarragon or lemon wedges if desired.