Pre-heat oven to 400 degrees F.
Toss carrots and potatoes with 2 tbsp oil, salt and pepper. Place in a baking pan and place in oven for about 25 minutes until tender. Remove and set aside.
Generously season the steak with salt and pepper. Cool oven down to 250 degrees F. Place steak on wire rack in a baking pan, wrap bones with foil and place in oven. Cook the steak until probe thermometer reaches 46 C (115 F), about 40 minutes.
Combine tarragon, parsley, garlic, chili flake, olive oil, pepper, salt to taste and vinegar.
While steak is cooking, add 1 pound of butter, 1 sprig thyme and 1 smashed garlic clove to a sauce pot and set on low.
Let butter infuse with aromatics for about 10 minutes. Now add the lobster and cook until warmed through, about 4 minutes.
Just before steak comes out of the oven, add 1 tbsp of oil to a cast iron skillet and heat on high until smoking.
Add 2 tbsp butter, 1 smashed garlic clove, 1 sprig thyme and rosemary to one side of the skillet. Add the steak and sear on both sides until well browned. Make sure to roll the edges of the steak so they get a nice caramelized crust as well.
Flash carrots and potatoes in oven to re-warm.
No need to rest steak, just slice and serve with warm lobster, carrots, potatoes and tarragon sauce.