Gently whisk eggs in a medium bowl and set aside. Chiffonade basil and set aside.
In a high-sided ovenproof pan, heat olive oil on medium. Once oil is hot, add chopped red onion and cook until soft, about 5 minutes. Add ham and cook for 1 minute. Add basil. Add salt and pepper to taste, and stir to combine.
Remove pan from heat and pour in whisked eggs. Place pan in the oven and bake for 12-14 minutes, or until the eggs are fully cooked. Remove from oven, loosen the sides with a knife and place whole frittata onto a cutting board or plate.
Top with cheddar cheese, slice into wedges and serve immediately.