Place ground beef and hot sausage in a large skillet over medium heat.
Cook, breaking up the meat, until browned and fully cooked.
Cut Velveeta into cubes while the meat is cooking.
Drain most of the grease from the skillet and return to heat.
Add Velveeta cubes to the skillet and cook, stirring until melted.
Stir in Worcestershire sauce, oregano, garlic salt, and salt.
Preheat the broiler to high.
Line a baking sheet with slices of party rye bread.
Spoon about 2 tablespoons of the cheese and meat mixture onto each bread slice.
Broil appetizers for 2–3 minutes until hot and bubbly, watching to avoid burning.
Alternatively, bake at 350°F for 15–18 minutes if not using broiler.
Garnish with chopped parsley if desired before serving.