Slice each chicken breast lengthwise to create thin cutlets. Place between two sheets of plastic wrap or parchment and gently pound until evenly thin.
In a small bowl, mix the smoked paprika, curry powder, and cumin. Season the chicken on both sides with the spice mix, followed by salt and pepper.
Heat the vegetable oil in a hot pan. Sear the chicken for 1½–2 minutes per side, until lightly golden. Transfer to a plate and keep warm.
Make the sauce:
Lower the heat slightly and add the butter to the same pan. Once melted, add the chopped shallot and sauté until softened.
Pour in the white wine, scraping up any caramelized bits, then add the chicken stock. Let the sauce bubble and reduce until slightly thickened.
Finish:
Stir in the fresh tarragon leaves. Taste and adjust seasoning.
Serve the chicken with the sauce spooned over, reserving some for the side.