Preheat the grill to maximum heat. Using a sharp knife, make about 10 cuts (5 mm deep) on each side of both trout. Rub with olive oil and season with salt and pepper. Finely grate the peel of 1 lemon and cut the fruit into slices. Stuff the belly cavities of the fish with chopped parsley and lemon wedges.
Place the trout side by side on a baking sheet or roasting pan. Scatter the grated lemon zest over the fish. Cut the second lemon in half and place the halves on the pan. Dot the trout with butter flakes.
Slide the pan under the grill, positioning the rack about 15 cm from the heat source. Grill for 6 minutes per side until the trout are crispy and golden brown.
Squeeze the roasted lemon halves over the fish. Serve with a simple, crunchy salad and Spanish white wine.