Heat your oven to 400 degrees. Then slice the shallots. Very finely chop 2 tablespoons of the shallot. Combine the finely chopped shallots with 1 tablespoon butter, the mustard, thyme, garlic, salt, and pepper to make the rub for the pork.

Getting the rub to stick on the pork might be a little challenging. I think patting the pork dry with a paper towel helps a bit. Evenly spread the rub on top of the pork coating all sides. Set aside.

Melt the remaining butter in a dutch oven (or similar) over medium heat. Add the mushrooms and sprinkle them with salt and pepper. Let cook for 2 minutes, and add the white wine, and let cook for another 3 minutes. Add the shallots and cook for an additional 3 minutes. Then pour the mushrooms and shallots into a bowl and set aside.

Increase the heat to high, and use the same dutch oven. Once it is hot, add the pork. You want to both brown the pork, while also preventing any drippings from burning. As the pork cooks, add chicken broth to the pan as necessary, and loosen any browned bits from the pan. (This process helps to make the gravy even more delicious). Once both sides of the pork tenderloin has browned (this takes about 4 minutes a side), add the mushrooms and shallots back into the pan. Add 1 cup of chicken broth to the pan. Then place the lid on the pot, and place it in the oven to roast for 12 minutes.

After 12 minutes, check the temperature of the pork and make sure it has reached 145 degrees. Cook for longer if necessary. Remove the pork from the pan and let it rest on a cutting board while you finish the sauce.

Heat the mushrooms, shallots, and all of the juices over medium-high heat to let it reduce. Whisk in the flour, and the cream. Let simmer and reduce for 3 minutes.

Slice the pork and serve it with the mushroom shallot gravy.