Heat 3 tablespoons oil in 12-inch oven-safe nonstick skillet over medium-high heat. Add chorizo; cook 5 minutes. Add onion and hashed browns to skillet. Cook 5 minutes more or until onion softens. Cover; reduce heat. Cook 8 minutes or until potatoes are tender.
Uncover; increase heat to medium-high and cook 4 minutes more or until potatoes are brown and crispy, stirring occasionally. Meanwhile, whisk together eggs, milk, salt and pepper in large bowl until frothy.
Pour egg mixture into skillet, shaking to distribute eggs evenly. Place skillet in oven; cook 12 to 15 minutes or until eggs are puffy and set.
Turn out frittata onto a cutting board; cool 30 minutes. Toss greens with remaining 1 tablespoon oil and lemon juice. Top frittata with greens. Cut into wedges to serve.