Glossy Shallot Tart

serves 6 to 8

1 ¼ cups all-purpose flour
1 stick (4 oz) cold, unsalted butter, cut into small pieces
about 4 Tbsp ice cold water
about 1½ cups dried beans or rice for baking tart shell
3 Tbsp sugar
1 Tbsp unsalted butter
10 to 16 shallots, peeled, separated into lobes, and halved
2 Tbsp sherry vinegar
4 oz spreadable chicken or duck liver mousse or, for vegetarians, walnut lentil paté

1
Pulse flour, butter, and ¼ tsp salt in a food processor until it forms a coarse meal. Pulse in water just until dough starts to get clumpy. Form dough into a disk, then wrap in plastic. Chill at least 1 hour or overnight.
2
Roll out dough to an 11-inch round and fit into a 9-inch tart pan with a removable bottom. Chill 1 hour.
3
Preheat oven to 375°F. Poke shell with fork tines, then line with foil and spread beans evenly on top. Bake 15 to 20 minutes until sides set. Remove foil with beans and bake until golden, about 15 minutes longer. Cool to room temp.
4
Place sugar, butter, ¼ tsp salt, and ½ cup water in a medium skillet. Add shallots, cut sides down, and bring to a simmer. Cover skillet with a tight-fitting lid and cook over medium-low heat, swirling pan occasionally, checking that there is still liquid, until shallots are tender, 10 to 14 minutes. (This can be done several hours ahead.)
5
Uncover skillet and cook, swirling pan occasionally, until liquid has evaporated and sugar is caramelized to a deep brown, about 10 minutes. Add vinegar and a few grinds of pepper. Swirl to combine and remove from heat. Spread mousse or paté in tart shell then arrange shallots on top and drizzle with caramel. Tart is best served warm.