Place the first 8 ingredients in a bowl and gently mix to combine. Use cold-water moistened hands to form 4 oval patties each about 3/4" thick. Heat 2 Tbsp. of the oil in a nonstick skillet set over medium heat. Cook the hamburger steaks 4 to 5 minutes per side, or until entirely cooked through.
While the hamburger steaks cook, heat the remaining oil in a small pot set over medium heat. Add the leeks and cook until tender, about 5 minutes. Add the stock/flour mixture, bring to a simmer, and simmer until a thickened gravy forms; season with salt and pepper. Serve the gravy with the hamburger steaks.