Preheat the oven to 200C/180C Fan/Gas 6. Put the garlic on a piece of kitchen foil and drizzle with the oil. Seal the foil into a parcel and roast for 30-40 minutes.
Meanwhile, put the chicken in a deep roasting tin and season with salt and pepper. Roast for 40-60 minutes.
While the chicken roasts, put the cream in a food processor with a whisk/paddle attachment and blend until it turns to butter, leaving the whey at the bottom. Spoon the solid part into a bowl, add a teaspoon of salt and mix. Squeeze the garlic cloves into the cream and mix again.
Smear the chicken with the garlicky cream and return it to the oven for 30-40 minutes, depending on the size of the bird. Check it is cooked through using a meat thermometer, or check that the juices run clear when the deepest part of the meat is pierced with a skewer.
Meanwhile, for the dauphinoise potatoes, preheat an oven to 170C/150C Fan/Gas 3½. Wash the potatoes in cold water to remove any excess starch. Drain well and pat dry.
Grease an ovenproof dish with 1 teaspoon of the butter and layer the potatoes in the dish, overlapping a little, until it is just full. Season with salt and pepper between each layer.
Put the cream and milk in a bowl, season with salt and pepper and whisk to combine. Pour this over the potatoes. Dot with the remaining butter, then cover tightly with kitchen foil and bake for 1 hour. Remove the foil and bake a further 30 minutes, or until golden-brown and tender.
Meanwhile, blanch the asparagus, peas and broad beans in a large saucepan of lightly salted boiling water. Drain and plunge into iced water to keep the colour. Melt the butter in a medium pan. Add the shallot and garlic and fry for 1-2 minutes. Add the blanched vegetables and cook for 2-3 minutes.
To serve, carve the roast chicken and place on a serving plate. Heat the gravy until hot through. Scoop a spoonful of the potatoes on to each plate, add the asparagus, peas and broad beans, and serve with the chicken and gravy.