Preheat oven to 350°F (180°C) with a rack in the center. Generously butter the entire inside of a 9 to 10 inch ceramic baking dish, then sprinkle in about a teaspoon of granulated sugar and tilt to coat, tapping out the excess.
Pit the peaches and slice each into 1/2 inch (1 cm) wedges, leaving the skins on or peeling as preferred. In a bowl, toss the slices with 1 tablespoon granulated sugar, the lemon zest, and 1 tablespoon flour until lightly coated.
Spread the coated peach slices in a single, even layer across the bottom of the prepared dish, leaving a little space between slices so the batter can puff up around each piece. Do not overcrowd the fruit.
In a large bowl, whisk the eggs with 1/2 cup granulated sugar and the salt until pale and smooth. Whisk in the vanilla, almond extract if using, and cooled melted butter, then pour in the milk and heavy cream and whisk until fully combined. Add the 2/3 cup flour and whisk just until smooth with no lumps; the batter should be thin, like crepe batter, so avoid over-whisking.
Slowly and evenly pour the batter over the arranged peaches, pouring gently to keep the fruit in place. If desired, sprinkle 1 tablespoon demerara sugar evenly over the surface for a crackly top.
Bake for 40 to 45 minutes, until puffed, deeply golden on top, and just set in the center. A thin knife inserted in the middle should come out clean or with only a few moist crumbs; if the top browns too fast, tent loosely with foil for the last 10 minutes.
Let the clafoutis cool for at least 10 to 15 minutes; it will deflate and sink as it cools, which creates the silky, custardy interior. Dust generously with powdered sugar, slice into wedges, and serve warm or at room temperature.