In a mixing bowl, cream together softened unsalted butter and icing sugar until smooth and fluffy, about 3-4 minutes. Beat in one egg until well incorporated, then gradually mix in plain flour until the dough begins to clump together. Shape the pastry into a disc, wrap it in plastic, and chill in the refrigerator for at least 2 hours until firm.

Preheat your oven to 350°F (175°C). Roll out the chilled pastry on a lightly floured surface to fit your tart pan. Carefully transfer the pastry to the pan, pressing into the edges. Line it with parchment paper and fill with pie weights or dried beans. Blind bake for 20 minutes, then remove the paper and weights and bake for an additional 5-10 minutes until lightly golden.

Peel, halve, and core the ripe pears. In a saucepan, combine water, granulated sugar, cinnamon sticks, and whole cloves, bringing to a gentle simmer. Add the pear halves and poach for approximately 15-20 minutes, or until soft but not falling apart. Remove the pears and simmer the poaching liquid until thickened, creating a lovely syrup.

In a large bowl, beat together granulated sugar and softened unsalted butter until creamy and light. Incorporate eggs, one at a time, followed by vanilla extract and ground cloves, mixing thoroughly. Gradually fold in almond meal and a touch of flour until combined.

Spread a generous layer of frangipane filling into the pre-baked tart shell. Slice the poached pear halves and arrange them artfully on top, fanning them for an elegant look. Brush the pears lightly with the spiced syrup.

Bake the assembled Pear Almond Frangipane Tart in the preheated oven for 60-70 minutes, or until the frangipane is golden brown and a toothpick inserted in the center comes out clean. Allow the tart to cool in the pan for about 15 minutes before transferring it to a wire rack to cool completely.