In a small skillet over medium heat, toast the pistachios until fragrant and they begin to release their oils, 3 - 5 minutes.
Season the pork tenderloin with salt and pepper and allow it to start coming to room temperature as you prepare the other ingredients. (You can remove it from the fridge up to one hour before you begin preparing the recipe.)
Slice the onions thinly. Chop the garlic cloves. Place a large, deep pan with a lid over medium high heat. Add olive oil and sauté onions until they are becoming translucent, 6-8 minutes. Season with a pinch of salt.
While the onions are cooking, cut the beets into thin slices, and cut the rounds into halves or quarters, depending on the size. Slicing them like this reduces the cooking time.
Add the sliced beets to the pan and continue to cook for another 7-10 minutes until the beets are beginning to soften. Add garlic and continue to cook for another minute or so until the garlic is fragrant. Season with a pinch of salt.
Add the wine, cider, and chicken stock and bring to a simmer. Season with a bit of salt, reduce heat to low, and cover the pan.
While the beets simmer, chop the apricots, mint and pistachios. Combine them with the lemon juice and olive oil and set aside.
After the beets have been simmering in the liquid for about 10 minutes, heat a non-stick skillet over medium high, add 1 tbsp of olive oil and sear the pork tenderloin on each side for 3 - 5 minutes, until golden brown. Make sure to get a quick sear on each end, too.
Nestle the pork tenderloins back into the simmering beets and cook uncovered for another 10-20 minutes, turning them from time to time. If the pan is getting too dry, add a splash of chicken stock. You want the final product to be a bit saucy. Cook until a meat thermometer registers 145 degrees F in the thickest part of the meat.
Allow the pork to rest for 5-10 minutes, then slice. Taste the beets and season with salt. Put some of the beet mixture on a plate, add slices of pork, then top with apricot-mint sauce.