Add the 3 tablespoons preserved lemon paste, the stock, butter, garlic, sugar, turmeric and half the cumin to a medium saucepan; place it over medium-high heat.
Bring to a boil and cook, stirring occasionally, for 15 minutes, until reduced by about a third.
Measure out roughly 3 tablespoons of the sauce into a small bowl, then add the cornstarch and whisk until there are no lumps.
Whisk this back into the sauce pot and cook for 1 minute, whisking continuously, until smooth and thickened slightly.
Remove from the heat.
Heat the oil, in a large high-sided frying pan, over a medium-high heat.
Once hot (a sprinkle of cornstarch dropped into the oil should sizzle right away), fry two of the chicken breasts for 3 minutes per side, or until nicely browned and just cooked through.
It should release easily from the skillet with a little help from a metal spatula.
Transfer to a paper towel-lined plate and continue with the remaining 2 breasts.
It might spit, so turn down the heat if needed.
Wipe out the frying pan, add the sauce and bring to a simmer over medium-high heat.
Add back all the chicken breasts and cook for just 3 minutes, gently turning them halfway.
Remove from the heat and stir in the 2 tablespoons of lemon juice.
Transfer the chicken breasts (cut them into strips, if you like) to a large serving platter with a lip and pour the sauce all over.
Sprinkle with the remaining cumin.
In a small bowl, toss together the spring onion, green onions and remaining 2 tablespoons of lemon juice; spoon this all over.