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Step 1
In a small bowl, combine the paprika and curry powder. Sprinkle the mixture over both sides of the chicken breasts. If time permits, cover and refrigerate for a couple hours.
Step 2
Lay the chicken breasts between two large pieces of plastic wrap and gently pound them until they are uniformly of 1/4-inch thickness. Season both sides liberally with salt.
Step 3
Preheat an over to 200F, and place a baking sheet with a cooling rack set over it in the center. In a large (14-inch) skillet, heat a film of canola oil over high heat until almost smoking. Lay two of the chicken breasts presentation (smooth) side down into the pan and cook until golden, 1-2 minutes. Flip the breasts and cook the other side until golden, being careful not to overcook the thin breasts. Transfer to the rack, add a little more oil to the pan if needed, and repeat with the other breasts.
Step 4
Pour out any remaining oil in the pan and add 1 tablespoon of butter. Add the shallot and cook until just soft, about 3 seconds, then add the wine and cook until reduced by half.
Step 5
Add the chicken stock, bring to a boil, and reduce until thickened to a sauce consistency. Stir in the chopped tarragon and remove from the heat. Add the remaining butter and swirl the pan until just melted into a glossy sauce. Pour in any accumulated juices on the baking sheet and swirl to combine.
Step 6
Arrange the chicken on a platter, pour the sauce over it, and serve immediately.