Step 1

Season the chicken on both sides with salt and pepper. In a 12-inch skillet over medium-high, combine the milk, tarragon sprigs, garlic, butter, peppercorns and 2 teaspoons salt. Bring to a simmer, stirring, then reduce to low and add the chicken in an even layer, submerging them. Cover and cook, adjusting the heat to maintain a gentle simmer (only a few bubbles), until the breasts are opaque throughout, 18 to 24 minutes, flipping them halfway through.

Step 2

Transfer the chicken to a cutting board. Pour the poaching liquid through a fine mesh strainer set over a medium bowl; reserve 2 garlic cloves and 3 tablespoons of the strained poaching liquid; discard the remaining solids and liquid.

Step 3

In a food processor, combine the tarragon leaves, parsley, capers, anchovies, vinegar, reserved garlic and reserved poaching liquid. Pulse until finely chopped, about 15 pulses. Add the oil and process until well combined, about 20 seconds.

Step 4

Cut the chicken breasts crosswise on the bias into ½-inch slices and arrange on a platter. Spoon the sauce over them.