To make the cake, heat the oven to 350°F with a rack in the middle position. Generously butter the bottom and sides of a 9-inch round cake pan. In a small bowl or liquid measuring cup, beat the eggs.

In a stand mixer with the paddle attachment, beat the butter, white sugar and lemon zest on medium until light and fluffy, 2 to 3 minutes, scraping the bowl as needed.

Add the almond flour and salt, then beat on medium just until incorporated, about 30 seconds. With the mixer running, gradually add the eggs and beat until homogenous, scraping the bowl as needed.

Increase to medium-high and continue to beat until the mixture is light and fluffy, about 3 minutes, scraping the bowl once or twice.

With the mixer running on low, gradually add the all-purpose flour and mix until incorporated, then slowly add the rum and beat just until combined.

Scrape the bowl to ensure no pockets of flour or rum remain. The batter will be thick.

Scrape the batter into the prepared pan, then spread in an even layer and smooth the surface. Bake until deep golden brown and the center of the cake springs back when gently pressed, 50 to 55 minutes.

Meanwhile, to make the rum syrup, in a large saucepan combine the white sugar, ⅓ cup water, allspice and peppercorns. Bring to a boil over medium-high, stirring to dissolve the sugar, then boil for 3 minutes.

Remove the pan from the heat and stir in the rum. Bring to a simmer over medium and cook for 2 minutes.

Pour the mixture though a fine mesh strainer set over a small bowl; discard the solids and set the syrup aside.

When the cake is done, let cool in the pan on a wire rack for 5 minutes. Invert the cake onto another wire rack; do not re-invert.

Immediately brush the top and sides of the cake with all of the rum syrup. Cool to room temperature, about 1 hour. Transfer the cooled cake to a platter.

To make the lemon glaze, in a medium bowl, whisk together the powdered sugar and salt, then gradually whisk in the lemon juice; the glaze should be smooth, with the consistency of yogurt.

If it is too thick, whisk in additional lemon juice ½ teaspoon at a time to attain the proper consistency.

Pour the glaze onto the center of the cake, then use an offset spatula or the back of a spoon to spread the glaze toward the edges, allowing just a small amount to drip down the sides.

Sprinkle with toasted almonds. Let stand at room temperature to set the glaze, about 1 hour.