Whisk egg yolk, cream, and vanilla together in bowl. Process flour, sugar, and salt in food processor until combined, about 5 seconds. Scatter chilled butter over top and pulse until mixture resembles coarse cornmeal, about 10 pulses. With processor running, add yolk mixture and process until dough just comes together, about 12 seconds.

Roll dough into an 11-inch circle on a lightly floured surface. Loosely roll dough around rolling pin and gently unroll into a 9-inch tart pan with removable bottom, letting excess dough hang over edge. Ease dough into pan by gently lifting edge of dough with your hand while pressing into corners and fluted sides of pan with your other hand (make sure edges are about ¼-inch thick). Run rolling pin over top of pan to remove any excess dough.

Wrap dough-lined pan loosely in plastic, place on a large plate, and freeze until dough is chilled and firm, about 30 minutes.

Adjust oven rack to middle position and heat oven to 375°F. Set dough-lined tart pan on baking sheet, discard plastic and line with a double layer of aluminum foil, covering edges to prevent burning but not tucking under pan; fill with pie weights or dried beans. Bake crust until golden brown and set, 20–25 minutes, rotating pan halfway through baking.

Remove weights and foil and bake until base of crust is dry to touch; about 5 minutes more.

Transfer crust to a wire rack to cool; decrease oven temperature to 350ºF.

Process almond flour, sugar, and salt in food processor until combined, about 10 seconds.

Add egg and egg white, almond and vanilla extracts; process until combined, about 10 seconds.

Add butter and process until no lumps remain, about 20 seconds. Scrape bottom and sides of bowl with rubber spatula and process to combine thoroughly, about 10 seconds more.

Transfer frangipane to a bowl; press a piece of plastic wrap onto surface of frangipane. Refrigerate until ready to use.

(Can be refrigerated in airtight container up to 3 days. Before using, let stand at room temperature about 10 minutes to soften; stirring it a few times to loosen the mixture up.)

For pears, combine apple, sugar, cardamom, and ginger in a saucepan; bring to a boil over high heat then reduce to a simmer over medium. Add pears, bring back to a simmer then reduce to a low simmer and cook, turning occasionally to ensure even poaching, until a toothpick inserted in the thickest part is met with light resistance, this can take anywhere from 20–40 minutes depending on type and size of pears, size of saucepan and heat. Some pears may be done before others—remove and transfer them to a bowl as they are finished cooking.

Remove saucepan from heat; gently remove pears to a bowl. Bring poaching liquid to a boil over high heat then reduce to medium-high and cook, stirring occasionally, until mixture is a deep amber color, reaches 230ºF, and measures ¾ cup, 15–25 minutes. Remove from heat and let cool completely.

Spread frangipane into pre-baked tart crust.

Cut pears in half lengthwise then cut crosswise into thin slices. Arrange pear slices over top of frangipane.

Bake tart at 350ºF until golden, 40–50 minutes.

Transfer tart to a wire rack and cool completely.