Add the olive oil to the pan and when hot, add the Brussels sprouts and diced apples. Saute for 8 minutes, stirring frequently until the Brussels sprouts brown and the apples start to tender.
Add the chicken stock and continue cooking until the stock cooks off and the apples are completely tender.
Add a pinch of the lemon zest, the juice from the lemon halves, dried cranberries and thyme. Season with salt & pepper, stir, taste and adjust seasonings.
Stir the caramelized onions back into the pan with the Brussels sprouts and apples. Again taste and adjust seasonings with salt & pepper.