Fry the chicken and bacon in the oil for 6–8 minutes, turning once or twice until golden and the chicken is cooked through.
Toast the bread on both sides, then spread with the mayonnaise. Divide the chicken and bacon between four slices of toast, then top with the sliced cheese. Cover the cheese with 4 more slices of toast, then add the tomato slices and watercress. Complete the sandwich stacks with the final slices of toast.
Press the sandwiches together, then cut each stack into 4 small triangles. Secure with cocktail sticks, if needed, and serve immediately.