Heat olive oil in a large 12-inch cast-iron or nonstick skillet over medium-high heat until shimmering appears. Add ground beef and cook 5-7 minutes, breaking into small crumbles while stirring occasionally until no pink remains.
Stir in diced potatoes, red bell pepper, and yellow onion directly into the beef mixture. Cook 8-10 minutes, stirring every 2-3 minutes so potatoes begin softening and edges achieve light browning.
Add zucchini, corn kernels, garlic powder, paprika, black pepper, and salt to the summer breakfast hash family recipe. Stir well and continue cooking 5-6 minutes until vegetables become tender-crisp.
Make four small wells in the hash mixture using the back of a spoon. Crack one egg into each well, then reduce heat to medium and cover the skillet 4-5 minutes until egg whites set completely.
Sprinkle shredded cheddar cheese across the entire skillet and let it melt 1-2 minutes uncovered. Garnish generously with fresh parsley and cayenne pepper, then remove from heat immediately.