Add the flour, sugar, salt, nutmeg, and cardamom to a food processor and pulse until combined, about 3 times for 3 seconds each. Add the butter and pulse off and on until the mixture looks a bit sandy in texture and the biggest pieces of butter are about the size of a grain of rice.

Whisk the egg yolk, cream, and vanilla extract together in a small bowl. Add the yolk mixture to the food processor and pulse 4 to 6 times for 2 seconds each. The dough will start to form on the bottom, but the top may look a little dry still and that’s totally fine.

Turn the mixture out onto a clean work surface and use your fingertips + to pinch the dough into a rough mass, working quickly. This shouldn’t take longer than 30 seconds. Take a handful of the dough and place it on the work surface. Then use the heel of your hand to apply gentle pressure and push the dough across the surface away from yourself. Set aside and repeat with the remaining dough.

Gather up all the bits of dough and form them into a ball, then pat into a circle and roll it out until it’s about an inch thick. Wrap in plastic wrap and refrigerate for 30 minutes to 1 hour.

Remove the plastic wrap and, on a well-floured surface, roll out the dough to be 3/16 inches thick before using a rolling pin to gently roll/wrap the crust loosely around the pin and *very carefully* transfer + unroll the crust onto a greased 10-inch tart pan. If it tears a bit, that’s okay. Press well into the edges and corners of the pan and repair any tears with excess dough. Trim any excess, poke the crust with a fork at 1-inch intervals. Then cover and freeze the pan for 30 minutes.

Preheat the oven to 400 degrees Fahrenheit. Remove the pan from the freezer and remove the plastic wrap. Line the inside of the crust with parchment paper and add pie weights or dried beans to weigh down the crust. Bake for 15 minutes, then gently remove the parchment paper and weights and place the tart crust back in oven at 350 degrees Fahrenheit for 7 minutes. Remove from the oven and brush the interior of the crust with egg white, then bake for another 10 minutes. Remove and set aside while you prepare the filling.

When making browned butter, it is best to use a stainless steel pan so that you can see the color of the butter change. Heat the butter in a large shallow frying pan over medium heat until it melts. Swirl the pan around a bit every couple minutes to help it cook evenly. Over a period of several minutes, you’ll notice the foam at the top of the butter start to change from light yellow to a light brown. Watch VERY closely, as it can go from being brown to burt very quickly. Once it reaches the light brown stage and the butter looks light brown and golden, smell it. It should smell nutty and similar to toffee. Remove from heat and set aside to cool to warm.

In the bowl of a stand mixer fitted with the whisk attachment, beat together the sugar and eggs at medium high speed until light and silky, about 3 minutes. Reduce speed to low and add the melted brown butter in a thin single stream sloooowly. If the butter is added too quickly and when too hot it can curdle the eggs, so take care. Add the honey, rum, vanilla extract and salt and mix until combined. Remove the bowl from the stand mixer and fold the flour into the batter until *just* combined, taking care not to overmix.

Preheat the oven to 350 degrees Fahrenheit. Place the tart pan (with the par-baked crust still inside) on a lipped baking sheet to make it easy to put in and remove from the oven. Arrange half the peach slices in a circular pattern on the bottom of the tart crust, then pour the batter over them. Then arrange the remaining half of the peach slices in a circular pattern so that they’re visible over the batter.

Place the pan in the oven and bake until the filling is golden and set, about 45 to 50 minutes. It should not be liquidy in the center, and you can test it by tilting the pan a bit towards you to see how much it moves. If there’s significant movement in the center, bake it another 5 to 10 minutes and check again. Remove from the oven and allow to cool on a wire rack for at least 1 hour before removing the tart from the pan. Slice and enjoy!