Scrub the sweet potatoes and cut each into six wedges. Spread out on a baking sheet, drizzle with 1 tbsp oil, season and roast at 200C/180C fan/gas 6 for 20 mins.
Lightly bash the breasts between two pieces of cling film until about 1cm thick. Put the chicken in a bowl and coat in the BBQ sauce. Add the chicken to the baking sheet, return to the oven for 10 mins, then crumble the cheese over the potatoes and bake for 5 mins more until bubbling.