Marinade the pheasant by crushing 2 garlic cloves and mixing with the lemon juice. Season well with salt and pepper and lay the breasts in this mixture for 30 minutes at room temperature.
Peel and thinly slice the onions and crush the remaining garlic. Melt the butter and 2 tablespoons of oil in a large sauté pan over a medium to high heat and add the onions and garlic. Cook stirring frequently for 25 minutes until the onions have caramelised and turned brown. Remove the leaves from the thyme and chop the dill including the stalks then add to the onions half way through cooking.
Wash the rice under cold running water until the water runs clear then add to the onions along with the spices and stir well. Then season with salt and pour over 425ml of boiling water. Stir, cover and leave to cook on a low heat for 30 minutes until the rice is cooked then remove from the heat.
While the rice is cooking heat the oven to 200C/400F/Gas 6 (180C fan). Heat a tablespoon of oil in a frying pan and brown the pheasant breasts on both sides, cover with foil before transferring to the oven to cook for a further 10 minutes.
Tip the pilaf rice onto a warm serving plate and top with the pheasant. Garnish with some dill sprigs and serve with natural yoghurt.