Preheat the oven to 180°C/160°C fan oven/gas mark 4. Melt half the butter in a pan and cook the shallots, garlic, thyme and sage with a pinch of salt until very soft. Add the vermouth and let it bubble until reduced by half.
Stir in the artichokes, olives and cream and bring to the boil. Season to taste.
Grease four 4cm x 10cm loose-bottomed tartlet cases with the remaining butter. Unroll the pastry on a floured work surface and cut four x 16cm diameter circles to line each case. Fit into each case, then divide the artichoke mixture among them. Using the remaining pastry, cut out 4 circles to cover the pies. Use some of the beaten egg yolk to brush the edge of the pastry. Top each pie with a lid and crimp the edges to seal.
Brush the pies with the rest of the beaten egg yolk, then bake for 30 minutes until golden brown and crisp.
Our thanks to Waitrose Cookery School Love to Cook (Simon and Schuster, £25) for providing this recipe.