For the almond crust: Preheat the oven to 350°F (175°C). Lightly grease a 9-in (23 cm) tart pan with a removable bottom. In a large mixing bowl, whisk the almond flour, flour, sugar, and salt together. Add the melted butter and egg and stir using a fork to incorporate to the dry ingredients. (The crust should be crumbly and damp-looking, with no visible traces of dry ingredients left.) Transfer the crust mixture to the prepared tart pan. Using your hands, carefully press the mixture down over the bottom and sides of the pan to form the crust. Bake for 20 minutes.
For the honey frangipane filling: In the bowl of a stand mixer, or in a large mixing bowl if you're using a hand mixer, beat the butter and honey together until fully incorporated, about 1 minute. Add one egg, beat to incorporate, then add the second egg. Mix in the almond extract. In a small bowl, whisk the almond flour and all-purpose flour together, then add to the butter and egg mixture. Mix just until combined. Transfer the frangipane mixture to the baked tart shell and spread into an even layer.
For the honeyed figs: Slice the figs in halves or quarters, depending on their size. Dip the cut sides of the figs into the warm honey, then set over the frangipane filling, cut side(s) up. Arrange the figs in a pretty pattern around the tart without overlapping them. Keep adding figs until the entire top of the tart is covered, without overcrowding.
Bake the fig frangipane tart for about 35 minutes, or until the center of the tart is puffed and firm, and the edges are golden. Transfer to a wire rack. To glaze, warm the honey and water together and whisk to combine. Use a pastry brush to gently brush the honey glaze all over the top of the tart. Let cool completely.
STORAGE: The fig frangipane tart will keep, covered, at room temperature for up to 2 days, or refrigerated in an airtight container for up to 5 days. (The crust will soften over time.) Always return the tart to room temperature or rewarm in a low oven for a few minutes before enjoying.
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