For the tart, cook the potatoes in a small saucepan of boiling water until just cooked through and leave to thoroughly drain in a colander. Heat 2 teaspoons of butter in a small frying pan and lightly sauté the apples until just soft. Once cool, thinly slice the potatoes and drain any liquid from the apples.
Preheat the oven to 200C/180C Fan/Gas 6. Line a large baking tray with baking paper.
Roll the pastry out into a 10cm/4 in circle on a lightly floured work surface. Spread the crème fraîche over the pastry, leaving a 1cm/½in border. Evenly space the potatoes, apples and fennel over the top of the tart, keeping the border around the edge. Season the top of the tart with salt and pepper and place the tart on the baking tray. Bake for 20 minutes, or until the pastry is cooked through and golden.
Meanwhile, heat the 10g butter in a frying pan and sauté the scallops for 1 minute on each side, or until they are lightly golden. Add the lemon juice and thyme and gently mix with the scallops.
For the dill cream sauce, heat the butter in a frying pan and sauté the shallots, garlic, thyme, star anise and bay leaf for 2–3 minutes. Add the lemon juice and cook until reduced. Add the vermouth and cook until the liquid is reduced by two thirds. Add the stock and cook again until the liquid is reduced by two thirds. Add the cream, season with salt and pepper and bring to the boil. Stir in the dill and remove from the heat. Remove the thyme, star anise and bay leaf.
Place the scallops on top of the tart, pour over the dill sauce and serve immediately.