Heat your oven to 350 degrees.

First, you want to sauté the onions, garlic, shallots, and mushrooms. Heat 1 tablespoon of olive oil in a dutch oven over medium heat. Add the onions and the garlic, and sauté for 2 minutes before adding the shallots and mushrooms. Add 1 teaspoon of thyme, 1 teaspoon of tarragon, 1/4 teaspoon of salt, and 1/8 teaspoon of black pepper. Stir to combine. Let cook for 3 minutes, then add 1 cup of white wine and let cook for another 3 minutes. Then remove from the dutch oven and set aside.

Rub the pork with 1 tablespoon of olive oil and then sprinkle with the remaining thyme and tarragon, plus a generous amount of salt and pepper. Turn the meat over and coat all sides.

Add just enough olive oil to coat the bottom of the dutch oven, and heat over medium-high heat. Once hot, add the pork and brown all sides, this will take about 2-3 minutes per side.

Once the pork has browned, return the sautéed onions, shallots, and mushrooms to the dutch oven. Pour 1 cup of white wine and 1 cup of chicken broth over. Bring to a simmer, and then place the lid on the dutch oven and place the pork in the oven. If you are using an in-oven thermometer, this is the time to insert it.

Cook the pork until it reaches 150 degrees. This will probably take 30-40 minutes.

You can simply serve the pork with the sauce as is, or you can thicken it into a gravy. To thicken the sauce into a gravy, remove the pork from the dutch oven and place on a cutting board. Strain out the mushrooms, onions, and shallots so that you are left with only the liquid. Melt 1 tablespoon of butter in the bottom of the dutch oven, and whisk in 1 tablespoon of flour. Return the liquid to the pot, and whisk to combine. Bring to a slow simmer, and let the gravy thicken. Return the mushrooms, onions, and shallots to the dutch oven and let them simmer in the gravy for 1 minute. For extra tender pork, thinly slice it and let it simmer in the gravy for about 30 minutes, adding more chicken broth if the gravy becomes too thick.