Preheat oven to 350 degrees Fahrenheit, and lightly grease a shallow baking dish with 1 tablespoon of the oil.
Heat 1 tablespoon of oil in a large skillet. Add the spinach, garlic, and vinegar, and cook until the spinach has wilted. Remove the skillet from the burner and allow the spinach to cool for about 5 minutes.
Stir the feta and lemon zest into the spinach mixture. Season with salt and pepper.
One at a time, place the chicken breasts on a piece of plastic wrap, folding the wrap over it. Use a kitchen mallet, flatten the breasts to about 1/4 inch.
Spread 1/4 of the spinach mixture over each chicken breast, and roll them up, fastening the ends with toothpicks.
Add the milk to a bowl.
In a second bowl, add the breadcrumbs and Romano cheese.
Dip each chicken breast first in the milk, and then in the breadcrumb mixture. Roll them and pat gently to get the breadcrumbs to stick.
Place the chicken breasts in the baking dish.
Melt the butter in a small saucepan. Once melted, stir in the lemon juice, and garlic, and pour it evenly over the chicken.
Bake for about 30 minutes, until cooked thoroughly.