Add the stock to a small bowl or measuring jug and sprinkle the gelatin over the top of it. Set aside until needed.
Pat the chicken breasts dry with paper towels and season generously with salt and pepper. Add the flour to a shallow bowl and dredge both sides of the chicken, ensuring it's completely covered, shake off any excess flour and set aside on a plate. Repeat with the remaining chicken breasts.
Add 2 tbsp of neutral oil to a large skillet (see note 2) and set over medium-high heat. Once just shy of smoking, add the chicken and cook on one side until it's browned, golden and releases easily from the bottom of the pan - about 2-3 minutes, before flipping and repeating on the other side. Remove from the pan and set on a paper towel-lined plate.
Reduce the heat to medium and add the shallot along with a generous pinch of salt. Cook until softened, about 2 minutes, before adding the garlic and lemon zest strips. Cook until fragrant, another 30 seconds.
Pour over the stock, scraping up any browned bits from the bottom of the pan. Bring to a simmer and allow to simmer for a few minutes, just to thicken the sauce a bit,
Whisking constantly, add the butter one piece at a time, ensuring that one piece melts comletely before adding the next. Stir in the capers, lemon juice, sherry vinegar, fish sauce and parsley. Taste to adjust for seasoning, adding salt and pepper where needed.
Add the chicken back into the pan and allow to warm through before serving, topping with more parsley if desired.
Notes
I use unsalted chicken stock in all my recipe development as it allows me to control the amount of salt going into the dish.
If possible, do not use a non-stick pan. Fond collection (browned bits on the bottom of the pan) is essential to building the pan sauce and not something possible without a little bit of sticking. I like stainless steel for this recipe.