A free-form tart that doesn't ask for a tin: a rough round of butter pastry, a spoonful of brown butter frangipane, and whatever peaches look best. Messy edges are the whole point.
Rub the cold, cubed butter into the flour, salt and sugar until it looks like coarse breadcrumbs with a few larger flecks of butter still visible — those flecks are what give you flaky layers later.
Add the ice water and vodka (the vodka keeps the dough tender without building gluten) and bring it together into a shaggy dough, adding the last of the water only if it needs it.
Tip the dough out and knead it a few times just to bring it together — it should feel hydrated, not sticky, and a few drier patches are fine, they'll even out as it rests.
Pat the dough into a disc, cut it in half, stack the halves and pat down again. Repeat this once more to build flaky layers, then wrap it and chill for 2 hours.
Brown the butter for the frangipane and let it cool fully to room temperature.
Beat the browned butter with both sugars and a pinch of salt, then mix in the egg and almond extract. Fold in the almond flour and flour last, just until combined.
Slice the peaches and toss with the lemon juice, cornflour, vanilla and icing sugar, then let them sit while you roll the pastry.
Roll the pastry between two sheets of baking parchment into a 35cm round, about 5mm thick. Heat the oven to 200°C with a baking sheet inside.
Spread the frangipane over the middle, leaving a ~5cm border, then arrange the peach slices on top in a loose circle or a few small fans.
Fold the border over the fruit, pleating as you go, then brush with the egg wash and scatter the brown sugar over the rim.
Slide the galette, still on its parchment, onto the hot baking sheet and bake for 30–35 minutes, until the pastry is deep gold and the fruit has softened.
Let it cool to room temperature, then warm the peach jam until runny and brush it over the fruit for shine.
Serve with whipped cream or ice cream.
The dough freezes well once wrapped, make a batch on a slow afternoon and you're one thawed disc away from this whenever the peaches at the market are finally good.