For the cake:
7/8 cup (140g) buckwheat flour
1 cup (140g) all-purpose flour
1/2 teaspoon plus 1/3 teaspoon flour
1/4 teaspoon ground cinnamon
1/2 pound (240g) unsalted butter, at room temp
1 cup (200g) sugar
4 large egg yolks
1 large egg
3/4 teaspoon vanilla extract
2 tablespoons dark rum
For the glaze
1 large egg yolk
1 teaspoon milk
Butter a 9 or 10-inch (25-cm) tart pan with a removable
bottom or a 9-inch/23 cm spring form cake pan). Preheat the oven to 350F degrees (180C).
In a small bowl, whisk together the buckwheat and all-purpose flour with 1/2 teaspoon salt and the cinnamon.
In the bowl of a standing mixer or by hand, beat the butter until light and fluffy. Add the sugar and continue to beat until smooth.
In a separate bowl, beat the 4 egg yolks and whole egg with the vanilla and rum with a fork, then gradually dribble the egg mixture into the batter while beating. If using an electric mixer, beat on high speed so the butter gets really airy.
Mix in the dry ingredients just until incorporated. Scrape the batter into the prepared pan and smooth the top as flat as possible with an offset metal or plastic spatula.
Make a glaze by stirring the single yolk and milk together with a fork, then brush it generously all over the top. (You may not use it all, but use most of it.) Take a fork and rake it across the top in three parallel lines, evenly space; then repeat starting from a slightly different angle to make a criss-cross pattern.
Crumble the remaining 1/3 teaspoon salt over the gateau with your fingers and bake for 45 minutes (hs note: you might want to place a rimmed baking sheet on the rack below your tart in case it leaks at all - also, don't over-bake or it will be on the dry side - start checking after 35 minutes or so). Let cool