Prepare the crust: In a food processor, pulse the flour and sugar. Add the cold butter and pulse until the mixture resembles coarse crumbs. Add the egg yolk and ice water, pulsing just until the dough starts to come together. Do not overmix.

Form the dough into a disc, wrap tightly in plastic wrap, and chill in the refrigerator for at least 30 minutes. Preheat your oven to 375°F (190°C). Roll out the chilled dough and carefully fit it into a 9-inch tart pan with a removable bottom. Trim the edges and prick the bottom with a fork.

Prepare the frangipane: In a medium bowl, cream together the softened butter and sugar until light and fluffy. Beat in the almond flour, egg, and vanilla extract until just combined into a smooth paste.

Assemble and bake: Spread the frangipane evenly over the bottom of the prepared tart shell. Arrange the halved or quartered fresh figs decoratively over the frangipane. Bake for 35-40 minutes, or until the crust is golden brown and the frangipane is set and lightly golden.

Glaze the tart: While the tart is cooling slightly, heat the apricot jam and water in a small saucepan until melted and smooth. Gently brush the warm glaze over the figs for a beautiful shine.

Cool completely on a wire rack before carefully removing the tart ring. Serve warm or at room temperature.