Because they use modernist ingredients, these amounts are given in metric by weight. For more information on how to measure modernist ingredients check out this article.
4-5 chicken breasts
Preheat the water bath to 141°F (60.5°C). If you don't have a sous vide machine, the chicken breasts can be grilled or pan seared.
Salt and pepper the chicken breasts then sprinkle with the rosemary. Seal them in a sous vide bag and place into the water bath. Cook for 2 to 4 hours. Remove from the sous vide pouches.
Cut the chicken into 0.5" to 1" (12mm to 25mm) portions and coat the chicken with the flour.
Fill a pan or pot with enough oil to come halfway up the chicken pieces then heat it to 375°F (190°C). Make sure the oil does not fill the pot more than halfway. Set up a cooling rack over a baking sheet.
Fry the chicken in the oil until just browned, about 60 seconds per side. Remove from the heat and place on the cooling rack then lightly salt and pepper the chicken.
Blend together the lemon juice, capers, and parsley then strain into a wide, flat-bottomed container. Blend the lecithin into the mixture. It can stay at this stage for a few hours.
Fill a pan or pot with at least a 1/2" to 1" (13mm to 25mm) of oil then heat to 375°F (190°C). Have a splatter screen ready, the capers can spit oil.
Dry the capers off and then using a long spoon, gently add the capers to the oil and cover with the splatter screen. Let cook until brown and crispy, about 1 to 2 minutes. Remove from the oil and let drain on paper towels.
First, foam the lemon-caper juice by running the immersion blender in it. Try to keep the blender halfway out of the liquid so the air is more easily incorporated. This can sometimes take up to 6 or 7 minutes and there will still be liquid left at the bottom of the bowl. Once there is a decent amount of foam on top, let it sit for 1 minute to stabilize.
Drizzle some olive oil on a plate then place a chicken piece on it. Sprinkle on some parsley leaves, add a fried caper or two and top with the lemon-caper air, lemon zest, and fresh ground pepper.