Heat oil in a large skillet over medium-high heat; add potatoes and cook 8–10 minutes until starting to brown.
Push potatoes to the side, add onion and bell pepper; cook 3–4 minutes until softened.
Add ground beef and garlic; break up and cook until browned. Stir together, season with paprika, thyme, salt, and pepper.
Make small wells and crack eggs into them; cover and cook 3–5 minutes until whites set and yolks reach desired doneness.
Sprinkle with parsley or green onion and serve straight from the pan.