To make the shallot compote, peel and finely slice the shallots, and finely chop the dates.
Heat the oil in a medium pan over a medium-low heat. Add the shallots and cook for 5 minutes, until tender. Stir in the mustard, balsamic, honey, sugar, dates and 115ml of water. Season well and reduce the heat to low.
Cook for 10 to 15 minutes, stirring occasionally, until the shallots have caramelised and the mixture has thickened. Remove from the heat and let it cool.
Preheat the oven to 200ºC/gas 6.
Trim and halve the parsnips, then peel and halve the shallots. Core and finely chop the apple.
Heat the goose fat and butter in a 22cm-wide ovenproof frying pan over a medium-low heat. Add the parsnips and shallots, cut-side down, and cook for 10 minutes, until they begin to caramelise.
Add the chestnuts and thyme sprigs, season well and cook for 5 minutes. Remove from the heat and top with about half of the shallot compote.
Roll out the pastry and trim it so it’s slightly bigger than your pan. Remove the pan from the heat and roll the pastry over the top, tucking it in the edges. Bake for about 30 minutes, until the pastry is golden and crisp on top.
Meanwhile, simmer the apple with 100ml of water in a small pan over a medium heat for 10 minutes, until softened. Season and stir in the balsamic.
Serve the tarte tatin hot with the apple balsamic sauce on the side.