Preheat oven to 375°F. Grease a loaf pan or line a sheet pan with foil.
Warm olive oil in a skillet over medium heat. Cook onion, pepper, and mushrooms until tender, 6–8 minutes.
Stir in garlic for 30 seconds. Transfer vegetables to a plate and let cool slightly.
Whisk milk, beaten egg, ketchup, Dijon, and Worcestershire in a large bowl. Mix in breadcrumbs and rest 3 minutes.
Add ground beef, salt, pepper, paprika, parsley, and cooled vegetables. Gently combine just until evenly mixed.
Shape into a loaf in the pan. Smooth the top. Brush with a spoonful of ketchup if you like a glaze.
Bake 35 minutes. Scatter half the provolone over the loaf and return to the oven.
Bake 10 minutes, add remaining cheese, then bake 5–10 minutes more until 160°F internal and cheese is melted.
Rest 10 minutes before slicing. Broil 1–2 minutes for extra bubbly cheese if desired.