I'm talking about the kind of restaurant that makes the kind of Italian-American classics that everyone grew up on as "Italian food". It's Italian food as intepreted by immigrants who had to cook their family recipes with the limitations presented to them by what was available in the U.S. They were also using new things that weren't available to them in Italy, but they liked. This was further refined and interpreted by their descendants.
These restaurants were once scoffed at as inauthentic by true aficionados of real regional Italian food, but they are finally getting their due. Italian-American food is a cuisine in itself and if done well, can still be delicious, whether they eat it in Italy or not.
A good red sauce place will always have certain dishes on its menu. There will be Chicken Cacciatore and Chicken Scarpiello. There will be Pork Chops Contadina and Steak Pizzaiola. There will be breaded chicken and veal cutlets (called "Milanese"). There will be Chicken, Veal, and Eggplant Parmigiana (and a good restaurant will spell it correctly). There will also be Chicken (and likely veal) Francese.
Why is it called Francese? What makes it French and why say French in Italian? ;-) It's a dish that is not just a favorite of your neighborhood Italian restaurant, but it's also a favorite of caterers. I even served it at my wedding. Although Chicken Francese can be interpreted a few different ways, it always contains eggs, butter, and lemon. This night I made it with garlic and white wine.
This recipe is so easy, you don't need a recipe.
Start with boneless, skinless chicken breasts that you have pounded a bit. You can use thighs too. Dredge them in seasoned flour and then dip them in egg.
Cook through in olive oil (about 2 tablespoons) and keep warm.
Add some garlic (about 4 cloves) and cook until fragrant.
Deglaze the pan with the juice of two lemons, a half a cup of white wine, and a half a cup of chicken broth. Allow to reduce a bit.
Add about two tablespoons of butter and swirl them in. Pour over warm chicken.
Serve with greens and maybe some roasted potatoes or pasta if you like.