Preheat the oven to 350 degrees F. In a large bowl, combine the ground beef, crushed saltine crackers, milk, 1 teaspoon of the salt, black pepper, Italian seasoning, and garlic powder. Mix gently until just combined.
Shape the mixture into 8 evenly sized oval patties. Place the flour in a shallow dish and stir in the remaining ½ teaspoon salt. Dredge each patty lightly in the seasoned flour, shaking off any excess.
Heat the oil and butter together in a large skillet over medium-high heat. Once the pan is hot, add the patties in batches and sear for 1-2 minutes per side, just until lightly golden. Do not cook through.
Arrange the seared patties in a single layer in a 9x13 inch baking dish. Set aside.
In a bowl, whisk together the cream of mushroom soup, whole milk, and Dijon mustard until smooth.
Pour the gravy evenly over the patties.
Cover the dish tightly with aluminum foil and bake for 35-45 minutes, or until the patties are cooked through and tender.
Garnish with chopped fresh parsley before serving, if desired.