Soak the bread. Add the bread cubes and milk to a bowl. Gently mix and press the bread with your hand so it absorbs the milk evenly and softens well.
Cook the onions. Melt 2 tablespoons of butter in a skillet over medium heat. Add the chopped onions and cook until softened.
Add the garlic. Stir in the garlic and cook for about 1 minute, just until fragrant.
Add the seasonings. Turn off the heat, then stir in the Dijon mustard, chopped parsley, and black pepper until everything is well combined.
Mix the beef mixture. Add the ground beef to a large bowl along with the soaked bread, onion mixture, egg, and salt. Mix everything thoroughly until the bread, onions, and seasonings are evenly distributed throughout the beef.
Shape the patties. Line a baking sheet with parchment paper and lightly grease it with oil. Wet your hands slightly, then shape the mixture into 6 large patties and arrange them on the prepared baking sheet.
Brush and bake. Brush the patties with some of the melted butter. Bake in a preheated 350°F (180°C) oven for 30 minutes.
Finish with butter. Remove the patties from the oven and brush them again with the remaining melted butter. Return them to the oven for another 5 minutes, until nicely browned and cooked through.