To make a walnut tarragon chicken tenders recipe, first you will need to prepare the ingredients. First, cut the chicken breasts in half lengthwise. Then, place the cut side down on the cutting board. Place the sliced walnuts into the bottom of the pan. Next, add the garlic, onion, and salt and pepper to taste. Cook the mixture over medium-high heat until the onions are translucent, about 5 minutes. Add the flour and stir to combine. Pour in the milk and mix well. Cover the saucepan with the lid and bring to boil. Reduce the heat to low and simmer for 20 minutes, or until thickened, stirring occasionally. Remove from heat and allow to cool slightly. Using tongs, transfer the tenderloins to the bowl of ice water and cover with plastic wrap. Allow to sit for 10 minutes before slicing.