Heat olive oil in a saute pan. Season turkey slices with salt and pepper. Add the fillets a few at a time and cooking a couple minutes each side until lightly browned and cooked through. Add extra oil if needed. Don't overcrowd the pan or the fillets will steam instead of brown. Move cooked slices to a warmed dish and tent loosely with foil to keep warm. Repeat until all the slices are cooked.
Once the turkey is cooked and set aside; add the broth to the pan and stir with a wooden spoon to loosen the browned bits from the bottom of the pan. Simmer the broth until it is reduced to about 1/2 cup. Whisk in the Dijon mustard and the lemon juice and bring just to a simmer. Add tarragon if using. Pour sauce over turkey and serve.