Step 1: Prepare the Pastry Crust : In a bowl, combine flour and sugar. Cut in cold butter using a pastry cutter or fingers until the mixture resembles coarse crumbs. Add egg yolk and cold water gradually until dough comes together. Form into a disc, wrap in plastic wrap, and chill for 20 minutes.
Step 2: Prepare Almond Frangipane : In a bowl, beat softened butter and sugar until creamy. Add almond flour, eggs, almond extract, and 1 tbsp flour. Mix until smooth. Set aside.
Step 3: Prepare Pears : Peel, core, and thinly slice the pears. Toss with lemon juice and optional sugar.
Step 4: Assemble the Tart : Preheat oven to 350°F (175°C). Roll out chilled dough on a floured surface to fit a 9-inch tart pan. Press into pan and trim edges. Spread almond frangipane evenly in the crust. Arrange pear slices decoratively on top, slightly overlapping. Sprinkle sliced almonds over the pears if desired.
Step 5: Bake : Bake for 35–40 minutes, until the frangipane is set and the crust is golden. Cool in the pan for 15 minutes before removing.
Step 6: Finish and Serve : Drizzle warm honey over the top of the tart just before serving. Slice into 8 pieces and serve at room temperature. Optional: Serve with a dollop of whipped cream or a scoop of vanilla ice cream.