Preheat oven to 350 degrees. Preheat your grill to 400-425 degrees.
Combine shallots, carrots, and garlic in a medium saucepot and cover with water.
Bring to a boil and cook until the carrots are tender, about 15 minutes. Reserve 2-3 T. of the water to puree.
While the carrots are cooking, bring the filet out of the fridge and pat complete dry with a towel or paper towels. This method will be grilling for char and flavor and finished in the oven.
Rub your filets with a small amount of olive oil on each side and generously season with salt and pepper.
Place filet on grill and do not touch and let grill for 2-3 minutes, turn filet to the left or the right and let grill for another 2-3 minutes (5-6 minutes on each side).
Flip steak and repeat.
Remove from grill and place on baking sheet and drizzle with olive oil and finish in oven for 3-5 minutes. (Medium steak 130F).
Take out oven and let rest for 5 minutes before slicing.
While the filet is resting, use a high-powered blender to blend the cooked carrots, olive oil, two tablespoons of water from the pot, salt, and pepper and puree until smooth and creamy.