To make the lemon syrup, combine water, sugar, lemon juice, and zest in a heavy saucepan and boil over medium-high heat until sugar dissolves. Lower the heat to medium and let the syrup simmer until the volume reduces to two thirds. Set aside and let it cool to room temperature.
While the syrup is being reduced, prepare the frangipane cream.
In a bowl of a stand mixer with the paddle attachment, beat the butter and confectioner's sugar on medium speed until creamy and fluffy.
Mix in the almond meal and continue beating.
Add in the vanilla, salt, rum, almond extract, and egg and beat until well combined.
Preheat the oven to 350˚F.
Line a baking sheet with parchment paper and arrange the brioche slices on the paper.
To assemble the bostocks, brush about 2 tablespoons of orange syrup onto the brioche slices.
Using an offset spatula, spread about 2 tablespoons of frangipane cream on top of the syrup.
Scatter about 2 tablespoons of sliced almonds on top of the frangipane cream.
Repeat the with remaining brioche slices.
Place the baking sheet in the oven and bake for 15-20 minutes until the sliced almonds are golden brown, the frangipane cream set, and the edges of the brioche caramelized.
Remove from the oven and let the bostocks cool for 5 minutes.
When ready to serve, sift a light flurry of confectioner's sugar over the bostocks.
The frangipane cream will keep in an airtight container in the refrigerator for up to a week.