Boil the potatoes until tender. Drain and mash with the roasted garlic, butter, and milk until silky. Cover and keep warm.

In a large bowl, combine the ground beef, diced onion, egg, breadcrumbs, salt, and pepper. Knead gently until just combined. Shape the mixture into four even, oval-shaped patties.

Heat oil in a large skillet over medium-high heat. Sear the patties until they have a dark, caramelized crust on both sides. Remove from the pan and set aside.

In the same skillet, melt the butter. Add the sliced mushrooms and sauté until they are tender and golden.

Stir the flour into the mushrooms and cook for 1 minute. Gradually whisk in the beef broth and the balsamic vinegar. Simmer until the gravy begins to thicken and coat the back of a spoon.

Return the steaks to the skillet. Reduce heat to medium-low and simmer for 5–10 minutes, allowing the meat to finish cooking and soak up the savory gravy.

Place a generous scoop of the roasted garlic mashed potatoes on a plate, top with a steak, and ladle plenty of the balsamic-mushroom gravy over the top.