For the potatoes:
1 ½ pound baby white or yellow potatoes
4 cloves garlic, crushed
¼ cup chopped fresh chives
3 tablespoons butter
For the gravy:
4 tablespoons butter, cut into pieces
¼ pound white mushroom caps, chopped or sliced
1 large or 2 medium onions, chopped
1 tablespoon fresh thyme or 1 teaspoon dried thyme
1 tablespoon thinly slice fresh sage or 1 teaspoon dried sage
1 bay leaf
Salt and pepper
3 tablespoons flour
2 cups beef stock
About 1 tablespoon soy sauce or shoyu
For the burgers:
1½ pounds ground sirloin
Kosher salt and coarsely ground black pepper
½ cup dried breadcrumbs
1 large egg, beaten
About 2 tablespoons Worcestershire sauce
2 tablespoons tomato paste, whisked with 3 tablespoons hot water
1 tablespoon dry mustard (a scant palmful)
1 teaspoon granulated garlic (1/3 palmful)
1 teaspoon granulated onion (1/3 palmful)
2 tablespoons olive oil
Finely chopped parsley, for serving
For the potatoes, in a large saucepan, cover the potatoes and garlic with water and bring to a boil. Salt the water and cook, uncovered, at a rolling boil until tender, about 12 minutes. Drain the potatoes and garlic and return them to the hot pot. Using a potato masher, coarsely crush the potatoes and garlic. Mix in the chives and butter; season with salt and pepper. Cover to keep warm.
For the gravy, in a large skillet, melt the butter over medium heat. Add the mushrooms and cook, stirring often, mushrooms are light caramel brown in color, 15 to 18 minutes; add onion, thyme, sage, and bay leaf and season with salt and pepper. Sprinkle with the flour. Cook, whisking often, until the flour is absorbed, about 1 minute. Whisk in the stock. Cook, whisking often, until thickened, 4 to 5 minutes. Season to taste with the soy sauce.
For the burgers, heat a large cast iron or non-stick skillet over medium-high. Place the beef in a large bowl; season with kosher salt and black pepper. Mix in the breadcrumbs, egg, Worcestershire, tomato paste, dry mustard, and granulated garlic and onion. Form the beef into 4 oval-shaped patties (thinner in the centers for even cooking).
Add oil, two turns of the pan, to the hot skillet. Cook the patties for 10 to 12 minutes, turning occasionally.
Serve the potatoes alongside the patties. Top the patties with the gravy and parsley.