Place a sheet of parchment paper over chicken breasts then gently flatten to 1cm/0.4 inch thick, with a meat mallet or rolling pin.
Drizzle with olive oil and season on both sides with salt and pepper.
Brown the chicken in a large skillet or deep frying pan. Cook until golden brown on both sides and cooked through. Remove from the pan and set aside.
Add the onion and garlic to the pan and cook for 1-2 minutes until fragrant then add the herbs. Cook for another minute.
Pour in the stock, cream and lemon juice and bring to a simmer. Add the broccoli, cover and allow to cook for 3-5 minutes or until the broccoli stems are just tender. Check by piercing them with a sharp knife.
Reduce the heat, add the cheese and allow to melt while stirring. Add the chicken back into the pan, spoon over the sauce, season to taste and serve.
If you prefer the sauce to be thicker, whisk 2 teaspoons corn starch / cornflour with a few tablespoons of water and add to the sauce when the broccoli is cooked. Allow to thicken then add the cheese to melt.