Melt butter and oil in a large flameproof casserole over high heat.
Fry pheasants until golden-brown all over then set aside.
Sauté onion and garlic in the same casserole for 4 minutes.
Stir in carrots and tarragon for 5 minutes then return pheasants breast-side down.
Add 150ml wine and season with salt and pepper.
Cover and cook on low heat for 1 hour, turning pheasants halfway through.
Boil 200ml milk then remove from heat and add saffron to infuse.
Scoop baked potato flesh into a pan with 45g butter and salt.
Mash the potatoes while gradually adding the saffron milk to reach desired texture.
Stir in 180g cooked sweetcorn and adjust seasoning.
Remove tender pheasants from the casserole and keep warm on a plate.
Add 100ml cream to the pan juices and simmer for 2 minutes.
Spoon the cream sauce over the pheasants and serve with the mash.