1 cup flour
1 Tbsp sugar
1/2 cup (aka 1 stick) unsalted butter, cold, cut into cubes
1 Tbsp ice water
1/2 tsp vanilla
1/8 tsp almond extract
1 cup heavy cream
1 cup sugar
1 cup sliced almonds (blanched or skin-on are both fine)
1/8 tsp almond extract
2 tsp orange or almond liquor (such as Grand Marnier, Triple Sec, or Amaretto)
optional: whipped cream and candied kumquats for serving (for the latter, just cut kumquats into thick slices, pop out the seeds (I find a skewer fairly helpful, but sometimes you can just squeeze them out), and simmer in a 1:1 sugar/water (or sugar/water & white wine) syrup until soft and translucent)
To make the crust: Mix together the flour and sugar. Using a food processor or pastry cutter, cut in the butter until it's reduced to rice-sized bits. Add the water and extract and work until the dough just comes together. Shape into a chubby disk, wrap with plastic and let rest in the refrigerator until chilled, about an hour.
After the dough has rested, remove and let come to room temperature. Using your hands, press the dough into a 9-inch tart pan until you form a thin-yet-relatively-even layer, pricking the bottom a few times with a fork to prevent it from bubbling up. Reserve a small bit of dough for patching any holes. Place the shaped crust in the freezer for about half an hour to chill thoroughly.
While the tart is freezing, preheat the oven to 375 degrees Farenheit. Bake the frozen shell until set and lightly golden, ~20-30 minutes (a bit of slumping is okay, but if it sinks too much, take it out mid-way and shape it back up). Remove and let cool slightly, patching any holes with the reserved dough (or just sort of smushing the partially-baked dough around to cover—it's fairly forgiving). Leave the oven on.
To prepare the filling, place the cream, sugar and salt in a large saucepan or pot, and bring to a boil over a high heat. When it foams up, turn off the heat and add the almonds, extract, and liquor. Stir to combine.
Pour the filling into the par-baked crust, and place it on a baking sheet. Bake in the pre-heated oven for 30 minutes until golden, with no remaining gooey white bits. After the first 10-15 minutes, tap the surface of the top a bit with a heat-proof spatula or wooden spoon, to keep it from forming an unattractive top crust. Repeat five minutes later, and again until the tart begins to set and become golden (if your tart happens to be bubbling over wildly, you needn't worry about this). Remove, and let cool for a few minutes. Remove from the ring and base—this may be a bit difficult if the tart has bubbled over and glued itself to both of them, but slip a small knife in until you can loosen it easily. Serve with whipped cream and candied kumquats, if desired, or enjoy as-is.