Pound chicken breasts to an even ½-inch thickness, pat dry, and season with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Cook chicken for 4–5 minutes per side, or until golden and the thickest part reaches 165°F (74°C). Transfer to a plate.
Reduce heat to medium. Add butter and shallots and cook for 3–4 minutes until softened. Add garlic and cook for another 30 seconds.
Pour in wine and scrape up the browned bits from the skillet. Simmer for 3–4 minutes, until reduced by about half. Stir in chicken broth and Dijon and simmer for 2 minutes.
Stir the cornstarch mixture again, add it to the skillet, and cook for 1–2 minutes, until the sauce lightly coats a spoon.
Remove the skillet completely from the heat and let it cool for 2–3 minutes. Whisk Greek yogurt until smooth, then gradually whisk about ¼ cup warm sauce into the yogurt. Slowly stir the tempered yogurt back into the skillet.
Stir in tarragon, lemon zest, and any chicken juices. Add lemon juice, salt, and pepper to taste. Return chicken to the skillet and spoon the sauce over it, warming gently for 1–2 minutes without letting the sauce boil.