Bring large pot of water to boil.
In bowl, mix egg yolks, 1/3 cup Pecorino Romano cheese and milk. Season with salt, to taste. Set aside.
In large skillet, heat olive oil and cook zucchini.
Cook pasta according to package directions. Reserve 1/2 cup cooking water.
Mix pasta in pan with zucchini. Add egg yolk mixture and 2 tablespoons cooking water. Combine well.
Add remaining cheese and mint; mix. Season with salt and pepper, to taste.