Heat oven to 375°. Place shallots in a bowl and cover with boiling water. Let them sit for 10 minutes to allow them to soften and to make peeling easier. Peel and halve shallots and set aside. Heat sugar in a large cast-iron or ovenproof skillet over medium heat and cook, swirling the pan occasionally, until it dissolves into a sticky caramel. Swirl in the butter, thyme, a splash of balsamic vinegar and a pinch of black pepper—take care, as the mixture will spit.

Remove the pan from the heat and put all the shallots into the pan, cut side down. On a lightly floured surface, roll out the pastry and cut out a round 1 inch larger than the pan. Drape the pastry over the shallots and tuck in the edges, so that it ‘hugs’ the shallots. Bake until the pastry is puffed and golden, 25 to 30 minutes. Set pan aside to cool for a few minutes, then invert the tarte onto a serving plate.