Preheat your oven to 425°F (220°C). Toss the sliced carrots in a bowl with 1 tablespoon of olive oil, salt, and pepper. Spread them on a baking sheet and roast for 15-20 minutes.

In a large pot, bring salted water to a rolling boil, then add linguine. Cook until al dente, about 8-10 minutes. Drain and set aside.

Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Season the steak with salt and pepper, then sear for 2-3 minutes on each side. Remove and rest.

In the same skillet, reduce heat and melt 4 tablespoons of butter. Add minced garlic and sauté until fragrant. Stir in lemon juice, Dijon mustard, and red pepper flakes.

Add drained linguine to the skillet, tossing to coat in the sauce. If too thick, add reserved pasta water. Fold in sliced steak and roasted carrots.

Serve in bowls topped with grated Parmesan and chopped parsley. Adjust seasoning with salt and pepper as needed.