First, rinse the bulgur in a strainer.
Bring the chicken stock to a boil in a small saucepan and stir in the bulgur. Remove it from the heat immediately and set aside for 20 minutes. Make sure you drain off any extra liquid.
Heat the olive oil in a skillet over medium heat. Cook the chopped mushrooms, chopped green onions and thyme for about 6 to 8 minutes, until the mushrooms are soft. Add in the balsamic vinegar and Worcestershire sauce.
Put the mushroom mixture in a food processor, along with the walnuts. Pulse until finely ground.
Stir in the cooked bulgur, the egg, the panko breadcrumbs and minced garlic.
Preheat the broiler on high heat and line a baking pan with aluminum foil. Give the foil a spritz with some nonstick spray.
Form the bulgur and mushroom mixture into 4 patties and arrange on the foil-lined baking sheet.
Broil for about 5 minutes per side.
Cook 4 eggs sunny-side-up in a skillet
Arrange the 4 burgers, the 4 sunny-side-up eggs, the sliced tomato and 4 tablespoons of ketchup on each of the hamburger buns.