6 tbsp. butter
2 large shallots, chopped
Salt and pepper
1 lb. green beans, trimmed
1 cup chicken stock
4 slices beef top round (1 1/4 lbs. total), pounded to about 1/4 inch thick
1 cup flour
1 tsp. ground sage
7 large organic eggs
2 tbsp. Dijon mustard
1 ½ cups fine dry breadcrumbs
Freshly grated nutmeg, about 1/4 tsp.
¼ cup canola or other neutral-flavored oil
1 lemon, halved
4 rounded tbsp. drained capers
8 anchovy fillets, drained
Preheat the oven to 200°. In a large skillet with a lid, melt 3 tbsp. butter over medium heat. Add the shallots and cook, stirring often, until softened, 3 to 4 minutes; season with salt and pepper. Add the green beans and toss to coat for a minute or 2, then add the stock. Cover and braise the beans until soft, 12 to 15 minutes more.
Season the beef and set up a breading station: Place the flour and sage in a shallow dish; season. In another shallow dish, beat 3 eggs and the mustard. In a third shallow dish, season the breadcrumbs with salt, pepper and the nutmeg. Working in batches, coat the steak in the flour mixture, then the egg mixture, and then the breadcrumb mixture, pressing to adhere.
In a large skillet, heat 2 tbsp. oil, two turns of the pan, and 1 tbsp. butter over medium-high. Add 2 cutlets and cook until browned and crispy, about 4 minutes per side. Place on a wire rack set inside a baking sheet; transfer to the oven to keep warm. Repeat with 2 more tbsp. oil, 1 tbsp. butter and the remaining cutlets. Wipe out the skillet; add the remaining 1 tbsp. butter and melt over medium-low heat. Crack in the remaining 4 eggs; cook until the whites are just set, about 3 minutes. Flip the eggs and cook until over easy, about 1 more minute.
To serve, divide the cutlets among plates. Squeeze the halved lemon over the cutlets. Top each cutlet with some capers, an over-easy egg and 2 anchovy fillets, crossed to form an X. Serve the green beans alongside.