Preheat your oven to 400°F for roasting the carrots.
Season the beef lightly with salt and pepper. In a heavy pan, heat olive oil over medium-high heat and sear the beef on all sides until browned.
Add the minced garlic and fresh thyme to the pan with the beef, stirring to combine.
Reduce the heat to low, add a splash of water or low-sodium broth if desired, and cover the pan. Let the beef braise gently for about 45 minutes, or until tender.
While the beef is braising, peel and cut the carrot into sticks. Toss them lightly with a small drizzle of olive oil, salt, and pepper and spread them on a baking sheet.
Roast the carrots in the preheated oven for 20-25 minutes until they are tender and slightly caramelized.
In a separate skillet, lightly sauté the sliced mushrooms over medium heat until they are tender and have released their moisture. Season with a pinch of salt and pepper.
To serve, arrange slices of the braised beef on a plate, top with the sautéed mushrooms, and add the roasted carrots on the side. Garnish with an extra sprinkle of fresh thyme if desired.