Heat a large sauté pan over high heat, add 2 Tbsp. of olive oil and cook mushrooms, stirring frequently, until they begin to brown. Transfer ¾ to a medium bowl and the remaining ¼ to a cutting board.

 Wipe pan clean with a paper towel, return to medium heat, add remaining 2 Tbsp. of olive oil, onions, and a pinch of salt and cook, stirring frequently, until tender and light caramel colored. Put ¾ of the onions in the bowl with the mushrooms, then add the garlic to the remaining onions and cook 2-3 minutes until fragrant. Transfer the onion/garlic mixture to the cutting board with the mushrooms and finely chop the mixture; set aside.

 In a large bowl, combine egg, half and half, and cracker crumbs and let stand 5 minutes. Add the chopped onion / mushroom mixture, ground meat, salt and pepper and combine thoroughly with your hands. Shape into six oval patties. Combine flour and cornstarch in a small shallow bowl and coat each patty thoroughly with the mixture, shaking off any excess.

 Heat a large skillet over medium-high heat, add the unsalted butter, and brown the patties on both sides. Remove and keep warm. Reduce heat to medium, add the wine to the skillet and deglaze, scraping up and brown bits left in the pan.  Add the tomato paste, mustard and thyme, and cook 1-2 minutes until fragrant. Whisk in the beef stock and Worcestershire then return onions, mushrooms, and patties to the skillet. Bring to a boil, reduce heat, cover and simmer 30 minutes, turning occasionally.