Heat a large skillet over medium-high heat and add olive oil if using lean beef.
Add chopped onion and bell pepper; sauté 3–4 minutes until softened.
Stir in minced garlic and cook 30 seconds until fragrant.
Add ground beef, break into pieces, and brown until no pink remains (5–7 minutes).
Drain excess fat if desired, leaving a tablespoon for flavor.
Reduce heat to medium and stir in tomato sauce, ketchup, brown sugar, Worcestershire sauce, and mustard.
Add smoked paprika, salt, and pepper; mix thoroughly to combine.
Bring mixture to a gentle simmer, then lower heat and cook 8–10 minutes, stirring occasionally, until sauce thickens.
Taste and adjust seasoning as needed (more sugar for sweetness, vinegar for tang, or salt).
Lightly toast hamburger buns, spoon hot sloppy joe mixture onto bottom buns, top with pickles or cheese, and cover with top bun.
Serve immediately while warm; garnish with chopped parsley if desired.