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Step 1
Butterfly chicken breasts and place each cutlet between two layers of plastic film and pound very thin and evenly. Season chicken with salt and pepper and set aside.
Step 2
On large dinner plate or tray, combine 1 cup of the flour with 1 tablespoon each salt and pepper and the Parmigiano. Pour the egg mixture into a wide dish with a high lip to avoid spills and set next to the seasoned flour mixture.
Step 3
Coat each thin cutlet thoroughly in flour mixture. Set aside.
Step 4
Add about 1/4 inch of olive oil into a deep frying pan set to medium-low heat. Add garlic cloves to oil, give the oil a quick swirl and let garlic sizzle slightly, being careful not to let it burn.
Step 5
One at a time, dip flour-coated cutlets into seasoned egg mixture, coating evenly, and carefully lay in pan, taking care to avoid covering the garlic and making sure the cutlet makes contact with the pan.
Step 6
Add 1/3 of the stick of butter to the pan and swirl pan to make sure butter is evenly distributed. When garlic begins to get nutty brown color, remove from pan and discard.
Step 7
Cook each cutlet approximately 3 minutes on each side, until somewhat golden-brown. Remove from pan and set aside on clean plate.
Step 8
Raise flame to medium and add 1/3 stick of butter to the same pan in which the chicken was cooked, and melt. Once butter is melted, add in the remaining 1/4 cup flour and keep stirring to mix thoroughly. Mixture should be a hazelnut-like, light brown color, and a uniform, paste-like consistency. This is your roux — do not let it get too dark or burn.
Step 9
Carefully add wine to skillet (it will sizzle and smoke) and let it cook for about 2 to 3 minutes, until all the alcohol cooks off and you are left with flavor. Take care to stir the mixture and scrape up the bits of fond (brown bits off the bottom of the pan) because that is pure, concentrated flavor.
Step 10
Add 2 cups of chicken stock and all of the lemon juice. Stir this mixture, ensuring all the bits have been lifted off the bottom of the pan.
Step 11
Raise heat to high until mixture begins to bubble and boil, and continue to stir. Once sauce boils, reduce the heat to medium-low and simmer for 2 minutes, stirring frequently.
Step 12
After 2 minutes, re-introduce chicken to sauce in the skillet. Cook for 5 minutes on one side, then flip each breast and cook for another 5 minutes.
Step 13
While chicken is simmering, butter brioche bun halves and toast. Set aside.
Step 14
Remove chicken from sauce, set on plate and while hot, top each cutlet with 1 spoon of sauce and then with chopped parsley.
Step 15
If you have a zester, add the zest of the lemon peels to the remaining sauce or — to use a technique from the great Ina Garten — just put the lemon "shells" bright-yellow-skin-side-down in simmering sauce to infuse additional lemon flavor.
Step 16
Place a chicken breast on the bottom bun. Top with a layer of sliced cornichon and layer 2 to 3 slices of honey ham over. Top ham with healthy amount of watercress but leave sandwich open-faced.
Step 17
Drizzle approximately 1 tablespoon of sauce over the watercress on each sandwich and add the top bun.
Step 18
If the consistency of the remaining sauce is too thick to serve as a dipping sauce, slowly add in more chicken stock until thin, dipping gravy consistency is achieved. Pour remaining sauce into four ramekins, one for each sandwich.
Step 19
Cut each sandwich diagonally (to ease the dipping process) and serve alongside lemon-wine-butter-stock dipping sauce for dunking.