- Make the crust: Using a food processor, pulse nuts with ½ cup flour until small crumbles form and the mixture resembles coarse beach sand. Add remaining flour, sugar, and salt and pulse to combine. Add butter and pulse until pea-size pieces form.
- In a small bowl, whisk together egg yolk, vanilla, and ice water. Slowly drizzle egg mixture into flour mixture while pulsing. Stop as soon as dough mostly comes together. Transfer dough to an airtight container and refrigerate for 1 hour.
- Transfer chilled dough to a greased tart pan. Press dough to create an even, smooth base with ¼-inch thick edge. Using a bench scraper or knife, flatten top of edges by pressing toward the tin’s edge. Freeze for 1 hour.
- Preheat oven to 350 degrees. Line tart shell with parchment paper and fill with pie weights or uncooked rice. Bake for 20 minutes, remove weights and parchment paper, then bake for another 10 minutes, until center is firm and crust is evenly golden brown but not dark. Remove from oven and set aside.
- Make the caramel sauce: In a medium saucepan, combine sugar and ½ cup water, letting water saturate most of the sugar. Without stirring, heat the mixture over medium heat until sugar dissolves. Increase heat to medium-high. Again, without stirring, cook mixture until it reaches an amber hue. At this point, give the pan a couple of swirls to evenly distribute amber color. This can take 8 to 12 minutes—keep a watchful eye the entire time. Once the mixture is dark amber in color but not burnt, remove from heat and whisk in heavy cream. Be careful; the mixture will sputter. Keep whisking until caramel is smooth—if clumps form, return to low heat and whisk until smooth. Stir in butter and a pinch of salt until smooth and glossy. Set aside and allow to reduce to room temperature and thicken.
- Make the oat crumble: To a medium bowl, add all ingredients except butter and whisk to combine. Add butter and, using your hands, incorporate butter into mixture using a snapping motion. When its ready, the crumble will turn darker brown, look wet, and butter will be evenly dispersed. Refrigerate until ready to use.
- Make the filling: To a large bowl, add all ingredients and toss to combine. Set aside.
- Assemble the tart: Preheat oven to 350 degrees. Place tart shell on sheet tray. Spread an even layer of caramel across bottom of the tart shell (about ¼ cup). Pour filling over caramel layer to reach ¼-inch above edge (it will cook down), discarding remaining liquid. Drizzle another ¼ cup caramel over filling. Top tart with an even layer of oat crumble, allowing some apple and pear to show through.
- Bake for 25 to 30 minutes, until crust is golden brown and center is bubbling. If edges are darkening before center is cooked, cover them with foil. Remove and cool on a wire rack. Serve with a scoop of vanilla or buttermilk ice cream and drizzle with remaining caramel sauce.