Preheat oven to 400 degrees F. Place peeled carrots on a baking sheet and toss in high heat avocado oil, salt and some garlic powder, to taste. Place in oven to roast for 25-30 minutes, depending on how you like your carrots (I like mine pretty burnt).
As soon as you get your carrots in the oven, place a cast iron skillet over medium-high heat and add 2 tablespoons of ghee. Once pan is very hot, pat filet mignon dry, sprinkle with salt and garlic powder on one side, then add to your hot pan. Once it's in the pan, salt and garlic powder the other side. Now leave it alone. Depending on the thickness of your filet mignon, you'll want to let the steaks cook for about 8-10 minutes per side. After 8 minutes, turn your steak and you should have a golden crust on the seared side. Cook for another 8-10 minutes. To get the perfect cooked steak, use a meat thermometer and remove steak from pan once it hits 145 degrees F, for medium rare. After you remove your steak from the pan, let it rest on a cutting board for 5-10 minutes. This resting period is very important because it will reabsorb all the juices and create a very tender, juicy and flavorful steak. Don't skip this part! Your lover will thank you.
While the steak cooks, make your béarnaise sauce. In a small skillet, add white wine, red wine vinegar, shallot and tarragon. Cook for about 5-8 minutes, until the liquid cooks off. Then pour the cooked shallot and tarragon into a tall mason jar or glass. Add 3 room temperature egg yolks. Place an immersion blender in the bottom of the glass, turn on then slowly pour the warm ghee to help emulsify the mixture. Once combine and thickened, fold in lemon juice, parsley, and salt!
Once steak has rested, serve up with roasted carrots and béarnaise on the side so your guest can choose however much they want to pour on top! Happy lovers day!