Combine herb butter ingredients in a small bowl until fully mixed.
Salt and pepper elk medallions generously and place back in fridge while vegetables cook.
If you have not already done so quarter your potatoes.
Put 3 T extra virgin olive oil in the skillet, or enough to coat the bottom.
Heat over medium heat until shimmering.
Add potatoes and sprinkle with kosher salt and pepper.
Cook for 20 minutes covered. Do not disturb.
Add asparagus, half of butter mixture, garlic, and thyme. Toss and cook until crisp ~10-15 minutes.
Add elk medallions and cover with the rest of the butter mixture. Cook about 3-4 minutes per each side basting with the butter.
You should pull the steaks at around 125°F and let rest for around ten minutes to get to medium rare. A instant read thermometer is very helpful for this.
Pull the skillet off the heat and enjoy!