Adjust oven rack to middle position and heat oven to 400 degrees F.
In a large bowl, whisk eggs, cheeses, oregano, salt and pepper to taste.
Heat oil and garlic in a large (12-inch) ovenproof nonstick skillet over medium-high heat until garlic starts to sizzle and turn golden. Add spinach and cook until excess moisture evaporates, about 1 minute. Add ham, shaking skillet to distribute evenly. Add egg mixture. Cook, without stirring, until eggs start to set around edges, about 1 minute.
Transfer pan to oven and bake until frittata is puffed and set, 10-12 minutes. Slide or invert onto a large plate, cut into wedges, and serve.