Heat 1 tablespoon butter and 1 tablespoon olive oil in large skillet over medium-high heat. Salt and pepper pork and then add the medallions to the skillet. Cook 2-3 minutes or until seared and browned on one side. Flip and cook another 2 minutes. Transfer the pork to a plate and set aside.
Melt the remaining butter and olive oil. Add shallots and garlic and cook for about 30 seconds. Whisk in flour until combined.
Deglaze the skillet with the chicken stock, scraping up any brown bits. Add milk and blue cheese and simmer until cheese is melted and sauce is thick, about 3 minutes.
Return pork to skillet and simmer in sauce for 4-5 minutes, or until pork is cooked through. Top with some fresh parsley and serve immediately.
Use a sharp knife to consistently cut the pork at the same thickness - about 2". If you vary the thickness of the pork, you will vary the cooking time.
Add cold oil to a cold skillet and let heat up to proper temperature before adding the chicken. You'll know it is ready when the oil starts to shimmer.
Control the amount of pungent flavor you like by selecting the right blue cheese. Mild is the least pungent but I usually go for a medium blue cheese. Just make sure to use a quality blue cheese.
You know the pork is cooked when it reaches 145°F with an instant-read thermometer or if you cut into the pork and the juices run mostly clear and it is mostly white with a slight hint of pink, it is good. I usually just cut the pork to see if it is done. If it isn't just cook slightly longer.
Leftovers will store well in the fridge for 2-3 days in an air-tight container or be frozen for 3 months.