Pat the pork tenderloins dry with paper towels. Trim away any silver skin with a small sharp knife, then sprinkle all sides with kosher salt and black pepper. Let the pork rest at room temperature for about 15–20 minutes while you prepare the cherry marinade.

In a medium bowl, combine the cherries, chicken broth, balsamic vinegar, honey, soy sauce, garlic, Dijon mustard, dried thyme, and red pepper flakes if using. Stir well and lightly mash a few cherries with the back of a spoon to help release their juices.

Place the seasoned pork tenderloins in a large zip-top bag or shallow dish. Pour about 1/2 cup of the cherry mixture over the pork and rub it on all sides. Set the remaining cherry mixture aside in the bowl to use later for the sauce. Marinate the pork in the refrigerator for at least 20 minutes and up to 4 hours.

When you are close to cooking, preheat the oven to 400°F (200°C). Place a rack in the center of the oven.

Heat a large oven-safe skillet over medium-high heat. Add the olive oil and butter. When the butter foams and just begins to brown, remove the pork from the marinade (discard the used marinade) and add the tenderloins to the hot pan. Sear for 2–3 minutes per side, turning until all sides are golden brown.

Transfer the skillet with the seared pork to the preheated oven. Roast for 12–18 minutes, turning the tenderloins once halfway through, until an instant-read thermometer inserted into the thickest part registers 140–145°F (60–63°C).

Remove the skillet from the oven and transfer the pork tenderloins to a cutting board. Tent loosely with foil and let rest for at least 10 minutes so the juices can redistribute.

While the pork rests, place the skillet back on the stove over medium heat, being careful of the hot handle. Pour the reserved cherry mixture into the pan, scraping up any browned bits from the bottom. Let the sauce simmer for 5–8 minutes, stirring occasionally, until the cherries soften and the liquid reduces slightly. For a thicker glaze, stir in the cornstarch slurry and simmer 1–2 minutes more until glossy and just thick enough to coat a spoon.

Taste the cherry sauce and adjust the seasoning. If it is too tangy, add a little more honey. If it is too sweet, add a splash of extra vinegar or a pinch of salt until the flavors are balanced.

Slice the rested pork tenderloin into 1/2-inch thick medallions. Arrange on a platter or plates and spoon the warm cherry sauce over the top, making sure each slice gets some cherries and glaze. Garnish with chopped fresh parsley or thyme if desired and serve immediately.