PEARS: Bring 4 cups water, sugar, and lemon juice to boil in large saucepan over medium-high heat, stirring until sugar dissolves. Add pears. Reduce heat to medium and simmer until pears are very tender, turning occasionally, about 20 minutes. Cool pears in syrup. Can be made two days ahead. Cover and refrigerate.
CRUST: Blend powdered sugar, almonds, and salt in processor until nuts are finely ground. Add butter and blend until smooth, scraping down sides of bowl occasionally. Mix in egg yolk. Add flour. Using on/off turns, blend until dough comes together in clumps. Gather dough into ball; flatten into disk. Wrap in plastic and chill at least 3 hours. Can be made two days ahead. Keep refrigerated.
FILLING: Finely grind almonds and flour in processor. Mix in 7 tablespoons sugar, then butter, blending until smooth. Mix in egg. Transfer filling to medium bowl. Cover and chill at least 3 hours. Can be made two days ahead. Keep chilled.
PUTTING IT TOGETHER: Once you’re ready to assemble all three components, position rack in center of oven and preheat to 375 degrees F. Roll out chilled dough on floured sheet of parchment paper to 12-inch round, lifting and turning dough occasionally to free from paper. Using paper as aid, turn dough into 9-inch-diameter tart pan with removable bottom; peel off paper. Seal any cracks in dough. Trim overhang to 1/2 inch. Fold overhang in, making double-thick sides. Pierce crust all over with fork. Freeze crust 10 minutes.
Line crust with buttered foil, buttered side down, then fill with dried beans or pie weights. Bake crust until sides are set, about 20 minutes. Remove foil and beans. Bake crust until sides are golden and bottom is set, pressing with back of fork if crust bubbles, about 10 minutes longer. Cool crust in pan on rack. Reduce oven temperature to 350 degrees F.
Spread almond filling evenly in crust. Stem pears and cut each in half lengthwise; scoop out cores. Cut each half crosswise into thin slices. Gently press each pear half to fan slices but keep slices tightly overlapped. Slide spatula under pears and arrange atop filling like spokes of wheel with narrow ends in center.
Bake tart until golden and tester inserted into center of filling comes out clean, about 55 minutes. Cool tart in pan on rack. Push pan bottom up, releasing tart from pan. Let stand at room temperature. Cut tart into wedges; sprinkle with powdered sugar, if desired, and serve.