In a medium bowl or large measuring cup, whisk together the heavy cream, white wine, chicken stock, minced shallots, Dijon mustard, chopped tarragon, kosher salt, black pepper, and olive oil or melted butter (if using) until the mixture is smooth and the mustard is fully incorporated.
Carefully ladle this one combined mixture over the raw pork tenderloins in the slow cooker, making sure the meat is well coated and the shallots and tarragon are distributed around and over the pork.
Cover the slow cooker with the lid and cook on LOW for 3 to 4 hours, or on HIGH for 1 1/2 to 2 hours, until the pork reaches an internal temperature of 145°F (63°C) and is tender but still sliceable. Try not to lift the lid during cooking so the pork stays moist and the sauce reduces gently.
Once the pork is done, transfer the tenderloins to a cutting board and tent loosely with foil to rest for about 5 to 10 minutes. This helps keep the juices in the meat instead of running all over the cutting board.
If you prefer a thicker sauce, in a small bowl stir together the cornstarch and cold water until smooth. Turn the slow cooker to HIGH. Stir the cornstarch slurry into the hot tarragon cream sauce in the slow cooker, cover, and cook for 5 to 10 minutes, stirring once or twice, until slightly thickened. Taste and adjust seasoning with a little more salt or pepper if needed.
Slice the rested pork tenderloin into 1/2-inch thick medallions. Arrange the slices on a serving platter or individual plates and spoon the warm tarragon cream sauce over the top. Serve any extra sauce on the side so everyone can help themselves.
Variations & Tips
For picky eaters, you can go light on the tarragon or even leave it out of the main mixture and just stir it into the sauce at the end for the adults. If your family is sensitive to onion flavors, swap the shallots for 1 to 2 teaspoons of onion powder so the sauce is smoother and milder. For a non-alcohol version, replace the white wine with extra chicken stock and a squeeze of lemon juice at the end to brighten the flavor. You can also add 8 ounces of sliced mushrooms to the slow cooker along with the pork if your crew likes them; they soak up the sauce beautifully. For a slightly lighter dish, use half-and-half instead of heavy cream, just know the sauce will be a bit thinner and may benefit from the optional cornstarch thickening step. If someone in the family doesn’t love mustard, reduce the Dijon to 1 tablespoon so it’s more of a background flavor. Leftovers reheat well with a splash of extra chicken stock or cream to loosen the sauce; they’re great served over noodles or tucked into toasted rolls for an easy next-day sandwich.
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